# MVP

2020

Randomized 2020

1 / 50

Choose the correct option

2 / 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:

3 / 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

4 / 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

5 / 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:

6 / 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?

7 / 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:

8 / 50

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

9 / 50

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

10 / 50

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

11 / 50

A differential equation is considered to be ordinary if it has

12 / 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:

13 / 50

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14 / 50

The number of permutations of n distinct objects is:

15 / 50

Chi‐square test CANNOT be applied to test the:

16 / 50

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17 / 50

For A, which one of the following is true

18 / 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

19 / 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:

20 / 50

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21 / 50

Non‐Parametric analogous of One‐Way ANOVA is:

22 / 50

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

23 / 50

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24 / 50

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25 / 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 :

26 / 50

Choose the correct option:

27 / 50

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

28 / 50

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

29 / 50

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

30 / 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

31 / 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:

32 / 50

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

33 / 50

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34 / 50

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

35 / 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:

36 / 50

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

37 / 50

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

38 / 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?

39 / 50

Choose the correct option:

40 / 50

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41 / 50

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

42 / 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:

43 / 50

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

44 / 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:

45 / 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,

46 / 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

47 / 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:

48 / 50

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

49 / 50

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

50 / 50

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