# DUET Resources

You can find Resources here.

• Habit Builder (25 Questions, 45 mins to make sure you build a habit of sitting and solving)

Habit Builder

1 / 25

Choose the correct option

2 / 25

If an unbiased coin is flipped till a first Head occurs, then the sample space is:

3 / 25

4 / 25

If Karl Pearson’s coefficient of skewness of a distribution is 0.32, its mean is 29.6 and standard deviation is 6.5, then mode of the distribution is:

5 / 25

6 / 25

The vectors (a1, a2) and (b1, b2) in R(2) are linearly dependent if and only if

7 / 25

Which of the following statement is correct?

8 / 25

The area enclosed by the curves y2 = x, y2 = 3x - 1 where 0 ≤ x ≤ 1/2 is:

9 / 25

For a 25 factorial experiment consisting of 23 blocks of size 22 each, the number of independent effect(s) confounded with blocks is/are

10 / 25

A system of 5 equations AX = b in 5 unknowns, has a solution if

11 / 25

The equation of tangents at origin to the curve x2(a2 - x2) = y2(a2 + x2) is:

12 / 25

The equation whose roots are cubes of roots of equation x3 - x = 0 is:

13 / 25

For any two events G and H, which of the following hold true?

14 / 25

If the observations recorded on five sampled items are 3, 4, 5, 6, 7 then unbiased estimate of the population variance is:

15 / 25

16 / 25

Choose the correct option

17 / 25

Measure of skewness of the Poisson distribution P(λ) is

18 / 25

An urn contains 3 white and 4 black balls. A ball is drawn at random, its color is noted and returned to urn along with two additional balls of the same color. If a ball is drawn again from the urn then the probability that the ball drawn is white is:

19 / 25

The joint probability function of two discrete random variables X and Y is given by, where x and y can assume all integers such that 0 ≤ x ≤ 2, 0≤ y ≤3, and f(x, y) = 0 otherwise. Then P(Y = 1 | X = 2) is

20 / 25

If y = sinpx + cospx then yn (the nth derivative of y w.r.t. x) equals

21 / 25

Choose the correct option

22 / 25

If events A and B are independent, consider the statements:

1. A and Bc are independent
2. Ac and B are independent
3. Ac and Bc are independent

Then:

23 / 25

The solution of the linear differential equation 2e3xdy/dx = 3e2y with y(0) = 0 is:

24 / 25

There are 3 persons A, B, C. The probability that A alone will survive for 10 years is 4/105 and the probability that C alone will die within 10 years is 2/21. Assuming that the events of the survival of A, B, C can be regarded as independent, the probability of surviving for 10 years of person B is:

25 / 25

The arithmetic mean of two regression coefficient bXY and bYX is______ the correlation coefficient between X and Y.

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• Mock 2020 (50 Questions, 90 mins)

Randomized 2020

1 / 50

Chi‐square test CANNOT be applied to test the:

2 / 50

A differential equation is considered to be ordinary if it has

3 / 50

The joint probability function of two discrete random variables X and Y is given by, where x and y can assume all integers such that 0 ≤ x ≤ 2, 0≤ y ≤3, and f(x, y) = 0 otherwise. Then P(Y = 1 | X = 2) is

4 / 50

Observe the following statements:

1. University roll number is measured in nominal scale
2. Marks obtained is measured in interval scale
3. Number of students admitted in the University during 2019‐20 is cross‐sectional data
4. University T shirt size measured in nominal scale

Which of the above statements given above is/are true?

5 / 50

If X ~ U(0,1) then Y = -2log(X) will follow

6 / 50

Let Xi, i= 1, 2,..., n, be a random sample from exponential distribution with parameter θ. Then a consistent estimator of   exp(-θ) is

7 / 50

If α, β, γ are the roots of x3 ‐ px2 + qx ‐ r=0, then the value of (α + β)(β + γ)(γ + α) is

8 / 50

Choose the correct option

9 / 50

Choose the correct option

10 / 50

For Poisson distribution with parameter μ, the value of measure of Skewness and measure of Kurtosis are:

11 / 50

For Normal curve, the Quantile Deviation, Mean Deviation and Standard Deviation are in the ratio:

12 / 50

The total number of factorial effects in a 2n factorial experiment is:

13 / 50

For A, which one of the following is true

14 / 50

Choose the correct option:

15 / 50

Let the equation of the regression lines be expressed as 2X ‐ 3Y = 0 and 4Y – 5X = 8. Then the correlation coefficient between X and Y is:

16 / 50

The coefficient of correlation between X and Y is 0.6. Their covariance is 4.8. If the variance of X is 9, then the standard deviation of Y is:

17 / 50

Choose the correct option

18 / 50

Choose the correct option

19 / 50

Choose the correct option

20 / 50

Choose the correct option:

21 / 50

The set W={( a1, a2, a3) : a1, a2, a3 ϵ R},  is not a subspace of R(3) , if

22 / 50

Choose the correct option

23 / 50

Which of the following is NOT TRUE about Neyman‐Pearson Lemma in hypothesis testing?

24 / 50

With the notation of combination, the value of 25C1 + 25C24/5 +5*49C0

25 / 50

Let Xi, i= 1, 2,..., n, be i.i.d random variables with E﴾Xi﴿=µ and var(Xi) < ∞. Consider an estimator Tn = 2* ∑ni=1iXi /n(n+1), for estimating µ. Then, Tn is,

26 / 50

While constructing a confidence interval for an unknown parameter using Pivotal quantity method, a pivotal quantity is defined as a

27 / 50

Based on a random sample of size n (X1, X2,..., Xn) from Cauchy(θ). A sufficient statistic for θ is

28 / 50

The vectors (a1, a2) and (b1, b2) in R(2) are linearly dependent if and only if

29 / 50

The number of permutations of n distinct objects is:

30 / 50

For any two events G and H, which of the following hold true?

31 / 50

Choose the correct option

32 / 50

Let A and B be events in a sample space S such that P(A) = 1/2, P(B) = 1/2, and P(Ac ∪ Bc ) = 1/3 then P(A ∪ Bc ) is:

33 / 50

Among the following system of equations

2x‐5y+7z=6,

x‐3y+4z=3,

3x‐8y+11z=11,

which one of the following is true?

34 / 50

Non‐Parametric analogous of One‐Way ANOVA is:

35 / 50

A population consists of four units 2, 4, 8 and 10. All possible samples of size 2 are drawn from this population by simple random sampling without replacement. Estimate of population mean and variance of the estimate of population mean is given by

36 / 50

Which of the following is an instance of non‐sampling error?

37 / 50

The key block of a 25 factorial experiment is given by:

[1, bc, de, bcde, abd, acd, abe, bce]

The confounded effects in this experiment are:

38 / 50

An experimental design which allows an unequal number of observations for each treatment under study is

39 / 50

The arithmetic mean of two regression coefficient bXY and bYX is______ the correlation coefficient between X and Y.

40 / 50

Let A1, A2, A3, A4 be the events of answering the questions 1, 2, 3 and 4 respectively such that P(A1) = 1/2, P(A2) = 1/4, P(A3) = 1/8, P(A4) = 1/16, then P(A1 ∪A2 ∪ A3 ∪A4) is:

41 / 50

The probability that a student passes a Multivariate test is 2/3 and the probability that he/she passes both a Multivariate test and Data Mining test is 14/45. The probability that he/she passes at least one test is 4/5. Then the probability that he/she passes the Data Mining test is:

42 / 50

If regression coefficients are given as bxy = 3.2 and byx = 0.8 then

43 / 50

The total yield of the treatments of a 22 factorial experiment replicated 4 times are:

 b0 b1 a0 20 44 a1 32 52

The simple effect of factor A at first level of B and the interaction effect AB can be estimated as

44 / 50

Choose the correct option

45 / 50

For a Latin square design with 5 treatments arranged in 5 rows and 5 columns, the observation corresponding to the second row, third column and the fourth treatment is missing. Total of known observations in the row and column corresponding to the missing observation are 125 and 265. Total of known observations receiving the fourth treatment and total of all known observations are 220 and 950 respectively. An estimate of the missing observation and the error degrees of freedom can be obtained respectively as:

46 / 50

If one flip a coin and then independently cast a die, then the probability of observing head on the coin and even number on the die is :

47 / 50

The total sales amount of a product from all 200 stores from last year was Rs 25,000. From a simple random sample of sales from 20 stores, the following data was obtained. Total sales amount for last year = Rs. 900 and total sales amount for the current year = Rs. 1205. The ratio estimate of the total sales for the current year will be:

48 / 50

The odds that a book on Linear Algebra will be favourably reviewed by three reviewers are 3 to 2, 4 to 3 and 2 to 3 respectively. Then the probability that out of three reviews only one review will be unfavourable is:

49 / 50

Let X1, X2,..., Xn be a random sample from U(‐θ, θ) distribution. Maximum likelihood estimator of θ is

50 / 50

A card is drawn from a well‐shuffled pack of 52 cards, then the probability of getting a heart or a king or a red card is:

0%
• Mock 2019 (50 Questions, 90 mins)

Randomized 2019

1 / 50

If ρ is the correlation coefficient between X and Y then the minimum value of Var(Y-aX) over all the values of a is given by:

2 / 50

If N = 60, (A) = 45, (B) = 35 and (AB) = 25 then the two attributes A and B are

3 / 50

4 / 50

If the mean deviation of x from its mean is 5 then the mean deviation of y = 2x + 3 from its mean is:

5 / 50

Given that the roots of the equation x3 - px2 + qx - r = 0 are in G.P. (geometric progression) then

6 / 50

7 / 50

How many two factor interactions are there in a 2×2×2 Factorial design?

8 / 50

9 / 50

The relationship between Pearson’s β and γ coefficients is

10 / 50

The difference between the expected value of a statistic and the value of the parameter is being estimated is called

11 / 50

Measure of skewness of the Poisson distribution P(λ) is

12 / 50

For a 25 factorial experiment consisting of 23 blocks of size 22 each, the number of independent effect(s) confounded with blocks is/are

13 / 50

The standard deviation of a distribution is 4. The value of the fourth central moment ( μ4) in order that the distribution be mesokurtic should be:

14 / 50

The regression lines of Y on X and of X on Y are Y = aX+b and X = cY+d, then the ratio of standard deviations of X and Y is

15 / 50

It is proposed to test H0: θ = θ0 against H1: θ = θ1 given a sample of size n from N (θ, 1). The critical region of the most powerful region depends on:

16 / 50

Which of the following statements regarding a binomial experiment is false, where n is the number of trials, and p is the probability of success in each trial?

17 / 50

Consider two urns. The first contains two white and seven black balls, and the second contains five white and six black balls. A fair coin is tossed and then draw a ball from the first urn or the second urn depending on whether the outcome was heads or tails. Then the probability that the outcome of the toss was heads given that a white ball was selected is:

18 / 50

The blood pressure (B.P.) of a group of patients was determined. After administering a medicine, the B.P. was measured again. To determine the significance of the medicine, the test to be applied is:

19 / 50

20 / 50

If the correlation coefficient between X and Y is +0.73, then the correlation coefficient between 3-2X and 5-3Y is:

21 / 50

22 / 50

The Central Limit Theorem is important in Statistics because:

23 / 50

24 / 50

Which one of the following statements about the derivability is NOT true?

25 / 50

If X is a binomial variate with parameters (5,θ) then an unbiased estimator of θ(θ - 1) is

26 / 50

Choose the correct option:

27 / 50

The tangent to the curve x(x2 + y2) = a(x2 - y2) at origin are

28 / 50

A system of 5 equations AX = b in 5 unknowns, has a solution if

29 / 50

30 / 50

Under proportional allocation in stratified sampling, the size of the sample from each stratum depends on:

31 / 50

Choose the correct option:

32 / 50

The general solution of exact differential equation (x2 - ay)dx + (y2 - ax)dy = 0 is

33 / 50

There are 3 persons A, B, C. The probability that A alone will survive for 10 years is 4/105 and the probability that C alone will die within 10 years is 2/21. Assuming that the events of the survival of A, B, C can be regarded as independent, the probability of surviving for 10 years of person B is:

34 / 50

Let X and Y be two variables and r(X,Y) be the correlation coefficient between them , then which of the following is always true?

35 / 50

Which one of the following tests is used for testing the randomness for a given sample?

36 / 50

If the scores (X) in Mathematics and (Y) in Statistics of ten students have the following summarized figure:

∑X = 60, ∑Y = 70, ∑X2 = 520, ∑Y2 = 650, ∑XY = 440

Then the correlation coefficient between the two scores is:

37 / 50

An unbiased die is tossed successively till a six occurs. The expected number of tosses required is:

38 / 50

39 / 50

Cayley Hamilton Theorem states

40 / 50

In any discrete series ( when all the values are different), the relationship between standard deviation (SD) and mean deviation (MD) is

41 / 50

If y = sinpx + cospx then yn (the nth derivative of y w.r.t. x) equals

42 / 50

A beta variable of the first kind with parameters (1,1) is:

43 / 50

If Karl Pearson’s coefficient of skewness of a distribution is 0.32, its mean is 29.6 and standard deviation is 6.5, then mode of the distribution is:

44 / 50

Let X and Y have the joint probability mass function P(X=x, Y=y) = 1/3x; y = 1,2,...,x; x = 1,2,3.

The value of conditional expectation E(Y|X = 3) is:

45 / 50

If the correlation coefficient of zero order in a set of 3 variates were equal to ρ each then the multiple correlation R21.23 is equal to:

46 / 50

ANOVA procedure is used for data that was obtained from four groups each comprised of five observations. The degrees of freedom for critical value of F are:

47 / 50

If the number of items produced in a factory during a week is a random variable with mean 100 and variance 400, then the probability that this week’s production will be at least 130 is:

48 / 50

The following system of linear equations

x1 + 2x2 + x3 = 3

2x1 + 3x2 + x3 = 3

3x1 + 5x2 + 2x3 = 1

has

49 / 50

For a 24 factorial experiment the principal block is ((1), ab, cd, abcd). The confounded effects are:

50 / 50

Choose the correct option

0%
• Mock 2018 (50 Questions, 90 mins)

Randomized 2018

1 / 50

The equation of tangents at origin to the curve x2(a2 - x2) = y2(a2 + x2) is:

2 / 50

If the area (under a normal density curve) to the left of the point x1 is 0.4 and and to the right of the point x2 is 0.3 then x1 and x2 are such that:

3 / 50

When there is rough linearity between the principal variable Y and the auxiliary variable X, but there is no proportionality, the link between Y and X can be exploited to improve simple random sample estimator by using:

4 / 50

Choose the correct option

5 / 50

In LSD with 5 treatments and one missing plot, the error degrees of freedom is:

6 / 50

Let X1, X2,...,Xn be a random sample from Cauchy distribution with location parameter θ and scale parameter 1. The Cramer Rao lower bound for unknown parameter θ, is:

7 / 50

Nine elements of which 4 are of one kind and 5 are of a different kind are arranged in a sequence. If R is the number of runs then P(R=2) is equal to:

8 / 50

If an unbiased coin is flipped till a first Head occurs, then the sample space is:

9 / 50

Choose the correct option

10 / 50

Choose the correct option

11 / 50

Variances of the sample mean under simple random sampling (Vran), under stratified sampling with proportional allocation (Vprop) and sampling with Neyman allocation (Vopt) obey which of the following order:

12 / 50

13 / 50

14 / 50

In a trivariate distribution, if r12 = r23 = r31 = ρ ≠ 1 then the value of R1.23 is

15 / 50

Let X follows exponential distribution with mean θ. For testing the null hypothesis H0: θ = 3 against H1: θ = 5, a test gives rejection region W0 = {x; x ≥ 4.5}. The size of the type-II error is:

16 / 50

If events A and B are independent, consider the statements:

1. A and Bc are independent
2. Ac and B are independent
3. Ac and Bc are independent

Then:

17 / 50

Interviewing all members of a given population is called:

18 / 50

19 / 50

Which of the following statement is correct?

20 / 50

In the context of characteristic function of a random variable, which one of the following statements is false?

21 / 50

Choose the correct option

22 / 50

If A is a non-singular matrix of order 4 × 4 and determinant of adj(A) is 4 then the value of |2adj(3A)| is:3

23 / 50

If the median of the distribution is 46 then the missing values of f1 and f2 are:

24 / 50

In analysis of variance problem involving 3 treatments with 10 observations each, SSE= 399.6. Then the MSE is equal to:

25 / 50

If the variability due to chance decreases, the value of F:

26 / 50

If correlation coefficient between two variables X and Y is 0.6 then the correlation coefficient between two new variables U = (X+6)/6 and V = (Y-6)/-6 is

27 / 50

An urn contains 5 red and 3 black balls. Balls are drawn one-by-one, with replacement till the 3rd red ball is drawn. The probability that the 3rd red ball occurs at the 5th draw is:

28 / 50

If R = Σi(xi - A)2i(xi - mean)2, A ≠ mean, then R is:

29 / 50

The equation whose roots are cubes of roots of equation x3 - x = 0 is:

30 / 50

The area enclosed by the curves y2 = x, y2 = 3x - 1 where 0 ≤ x ≤ 1/2 is:

31 / 50

Suppose that the five random variables X1, X2,..., X5 are independent and each has standard normal distribution. A constant c such that the random variable c(X1 + X2)/(X32 + X42 + X52)1/2 will have a t-distribution has value:

32 / 50

If ANOVA procedure is applied to the data obtained from 5 samples, where each sample contains 9 observations, then the degrees of freedom for critical value of F are:

33 / 50

34 / 50

The area under a normal curve between one standard deviation on either side of the mean is:

35 / 50

If the observations recorded on five sampled items are 3, 4, 5, 6, 7 then unbiased estimate of the population variance is:

36 / 50

What is Spearman's Rank Correlation Coefficient?

37 / 50

The listing of elements in population with distinct identifiable number is classified as:

38 / 50

If vr is the absolute moment of order r about origin zero of a distribution then:

39 / 50

Let x1 = 2.4, x2 = 9.2, x3 = 5.2, x4 = 4.1, x5 = 2.1 and x6 = 3.1 be the observed values of a random variable of size 6 from uniform distributions with parameters (θ - 2, θ + 6) where θ > 0 is unknown then MLE of θ is:

40 / 50

Suppose that p(x,y), the joint probability mass function (p.m.f.) of discrete random variables X and Y, is given by:

p(0,0) = 0.4, p(0,1) = 0.2, p(1,0) = 0.1, p(1,1) = 0.3

Then the conditional p.m.f. of X given that Y = 1 is:

41 / 50

The value of lim x —>0 axbx - bx - ax - 1/x2 is:

42 / 50

The solution of the linear differential equation 2e3xdy/dx = 3e2y with y(0) = 0 is:

43 / 50

The ages of 7 family members are 2, 5, 12, 18, 38, 40 and 60 years respectively. After 5 years a new member aged x years is added. If the mean age of the family now goes up by 1.5 years, then the value of x (in years) is:

44 / 50

Choose the correct option

45 / 50

An urn contains 2 white and 3 red balls. 15 balls are drawn one-by-one with replacement. The standard deviation of the number of white balls drawn is:

46 / 50

In case of two attributes A and B if (A) = 30, (B) = 40, N = 200, then for A and B to be negatively associated the frequency of the class AB will be:

47 / 50

The estimator T0 is MVU estimator for γ(θ) and T1 is any other unbiased estimator for γ(θ) with efficiency 0.0169. The correlation between T0 and T1 is:

48 / 50

Choose the correct option

49 / 50

An urn contains 3 white and 4 black balls. A ball is drawn at random, its color is noted and returned to urn along with two additional balls of the same color. If a ball is drawn again from the urn then the probability that the ball drawn is white is:

50 / 50

Suppose that there is a chance for a newly constructed building to collapse, whether the design is faulty or not. The chance that the design is faulty is 10%. The chance that the building collapses is 95% if the design is faulty and otherwise it is 45%. If it is seen that the building has collapsed, then the probability that it is due to faulty design is:

0%
• Master Test (50 Questions, 90 mins, has questions from all three past year papers)

Master Paper

1 / 50

The Central Limit Theorem is important in Statistics because:

2 / 50

It is proposed to test H0: θ = θ0 against H1: θ = θ1 given a sample of size n from N (θ, 1). The critical region of the most powerful region depends on:

3 / 50

If N = 60, (A) = 45, (B) = 35 and (AB) = 25 then the two attributes A and B are

4 / 50

Let X follows exponential distribution with mean θ. For testing the null hypothesis H0: θ = 3 against H1: θ = 5, a test gives rejection region W0 = {x; x ≥ 4.5}. The size of the type-II error is:

5 / 50

Choose the correct option

6 / 50

Choose the correct option:

7 / 50

8 / 50

Choose the correct option

9 / 50

There are 3 persons A, B, C. The probability that A alone will survive for 10 years is 4/105 and the probability that C alone will die within 10 years is 2/21. Assuming that the events of the survival of A, B, C can be regarded as independent, the probability of surviving for 10 years of person B is:

10 / 50

In any discrete series ( when all the values are different), the relationship between standard deviation (SD) and mean deviation (MD) is

11 / 50

Suppose that the five random variables X1, X2,..., X5 are independent and each has standard normal distribution. A constant c such that the random variable c(X1 + X2)/(X32 + X42 + X52)1/2 will have a t-distribution has value:

12 / 50

The total sales amount of a product from all 200 stores from last year was Rs 25,000. From a simple random sample of sales from 20 stores, the following data was obtained. Total sales amount for last year = Rs. 900 and total sales amount for the current year = Rs. 1205. The ratio estimate of the total sales for the current year will be:

13 / 50

If the area (under a normal density curve) to the left of the point x1 is 0.4 and and to the right of the point x2 is 0.3 then x1 and x2 are such that:

14 / 50

Which of the following statements regarding a binomial experiment is false, where n is the number of trials, and p is the probability of success in each trial?

15 / 50

Cayley Hamilton Theorem states

16 / 50

An urn contains 5 red and 3 black balls. Balls are drawn one-by-one, with replacement till the 3rd red ball is drawn. The probability that the 3rd red ball occurs at the 5th draw is:

17 / 50

The ages of 7 family members are 2, 5, 12, 18, 38, 40 and 60 years respectively. After 5 years a new member aged x years is added. If the mean age of the family now goes up by 1.5 years, then the value of x (in years) is:

18 / 50

Which of the following statement is correct?

19 / 50

Based on a random sample of size n (X1, X2,..., Xn) from Cauchy(θ). A sufficient statistic for θ is

20 / 50

Choose the correct option

21 / 50

Let X and Y be two variables and r(X,Y) be the correlation coefficient between them , then which of the following is always true?

22 / 50

A population consists of four units 2, 4, 8 and 10. All possible samples of size 2 are drawn from this population by simple random sampling without replacement. Estimate of population mean and variance of the estimate of population mean is given by

23 / 50

The probability that a student passes a Multivariate test is 2/3 and the probability that he/she passes both a Multivariate test and Data Mining test is 14/45. The probability that he/she passes at least one test is 4/5. Then the probability that he/she passes the Data Mining test is:

24 / 50

If events A and B are independent, consider the statements:

1. A and Bc are independent
2. Ac and B are independent
3. Ac and Bc are independent

Then:

25 / 50

Suppose that p(x,y), the joint probability mass function (p.m.f.) of discrete random variables X and Y, is given by:

p(0,0) = 0.4, p(0,1) = 0.2, p(1,0) = 0.1, p(1,1) = 0.3

Then the conditional p.m.f. of X given that Y = 1 is:

26 / 50

Choose the correct option

27 / 50

Let x1 = 2.4, x2 = 9.2, x3 = 5.2, x4 = 4.1, x5 = 2.1 and x6 = 3.1 be the observed values of a random variable of size 6 from uniform distributions with parameters (θ - 2, θ + 6) where θ > 0 is unknown then MLE of θ is:

28 / 50

What is Spearman's Rank Correlation Coefficient?

29 / 50

Choose the correct option

30 / 50

If the scores (X) in Mathematics and (Y) in Statistics of ten students have the following summarized figure:

∑X = 60, ∑Y = 70, ∑X2 = 520, ∑Y2 = 650, ∑XY = 440

Then the correlation coefficient between the two scores is:

31 / 50

If vr is the absolute moment of order r about origin zero of a distribution then:

32 / 50

When there is rough linearity between the principal variable Y and the auxiliary variable X, but there is no proportionality, the link between Y and X can be exploited to improve simple random sample estimator by using:

33 / 50

Measure of skewness of the Poisson distribution P(λ) is

34 / 50

Choose the correct option

35 / 50

Which one of the following statements about the derivability is NOT true?

36 / 50

Choose the correct option

37 / 50

While constructing a confidence interval for an unknown parameter using Pivotal quantity method, a pivotal quantity is defined as a

38 / 50

If regression coefficients are given as bxy = 3.2 and byx = 0.8 then

39 / 50

A beta variable of the first kind with parameters (1,1) is:

40 / 50

For a 24 factorial experiment the principal block is ((1), ab, cd, abcd). The confounded effects are:

41 / 50

42 / 50

The key block of a 25 factorial experiment is given by:

[1, bc, de, bcde, abd, acd, abe, bce]

The confounded effects in this experiment are:

43 / 50

Let X and Y have the joint probability mass function P(X=x, Y=y) = 1/3x; y = 1,2,...,x; x = 1,2,3.

The value of conditional expectation E(Y|X = 3) is:

44 / 50

If A is a non-singular matrix of order 4 × 4 and determinant of adj(A) is 4 then the value of |2adj(3A)| is:3

45 / 50

The vectors (a1, a2) and (b1, b2) in R(2) are linearly dependent if and only if

46 / 50

The difference between the expected value of a statistic and the value of the parameter is being estimated is called

47 / 50

Let Xi, i= 1, 2,..., n, be a random sample from exponential distribution with parameter θ. Then a consistent estimator of   exp(-θ) is

48 / 50

Let A1, A2, A3, A4 be the events of answering the questions 1, 2, 3 and 4 respectively such that P(A1) = 1/2, P(A2) = 1/4, P(A3) = 1/8, P(A4) = 1/16, then P(A1 ∪A2 ∪ A3 ∪A4) is:

49 / 50

Chi‐square test CANNOT be applied to test the:

50 / 50

Given that the roots of the equation x3 - px2 + qx - r = 0 are in G.P. (geometric progression) then