MVP 2020 Randomized 2020 1 / 50 Choose the correct option 4 2 1 3 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: 7.12 2.67 3.05 5.23 3 / 50 If α, β, γ are the roots of x^{3} ‐ px^{2} + qx ‐ r=0, then the value of (α + β)(β + γ)(γ + α) is pq qp – r q^{2} – 2pq pq + r 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 (6, 3.33) (6, 5) (6, 10) (10, 3.33) 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: Rs. 18,672 Rs. 33,472 None of these Rs. 18,075 6 / 50 Observe the following statements:University roll number is measured in nominal scaleMarks obtained is measured in interval scaleNumber of students admitted in the University during 2019‐20 is cross‐sectional dataUniversity T shirt size measured in nominal scaleWhich of the above statements given above is/are true? 3 only 1 and 2 only All are true 1 only 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: 1/9 5/6 2/3 4/9 8 / 50 With the notation of combination, the value of ^{25}C_{1} + ^{25}C_{24}/5 +5*^{49}C_{0} 5 20 25 35 9 / 50 If regression coefficients are given as b_{xy} = 3.2 and b_{yx} = 0.8 then Sign of one coefficient should have been in negative Given values of regression coefficients are not possible Both coefficient should be greater than unity Regression coefficients have correct values 10 / 50 The total number of factorial effects in a 2^{n} factorial experiment is: None of these 2^{n} – 1 2^{n} 2^{(n-1)} 11 / 50 A differential equation is considered to be ordinary if it has More than one dependent variable More than one independent variable One independent variable One dependent variable 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: 70/175 157/175 1/93 24/175 13 / 50 Choose the correct option 2 4 1 3 14 / 50 The number of permutations of n distinct objects is: n!/(n-1)! 1/(n-1)! n!/(n-n)! 1 15 / 50 Chi‐square test CANNOT be applied to test the: Significance of regression coefficient Goodness of fit Independence of attributes Equality of two population variances 16 / 50 Choose the correct option 1 3 2 4 17 / 50 For A, which one of the following is true λ=1 and 2 are the eigen‐values corresponding to A λ=2 and 4 are the eigen‐values corresponding to A v_{1}=(2, ‐1) and v_{2}=(1, 1) are the eigen vectors corresponding to A v_{1}=(2, 1) and v_{2}=(‐1, 1) are the eigen vectors corresponding to A 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 exp(-sample mean) exp(-1/sample mean) sample mean exp(1/sample mean) 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: √8/15 √15/8 √15/4 √7/15 20 / 50 Choose the correct option 4 2 3 1 21 / 50 Non‐Parametric analogous of One‐Way ANOVA is: Kruskal‐Wallis test Wilcoxon Signed Rank Mann‐Whitney test Friedman test 22 / 50 For Normal curve, the Quantile Deviation, Mean Deviation and Standard Deviation are in the ratio: 12:5:17 3:4:5 10:15:12 10:12:15 23 / 50 Choose the correct option 3 1 4 2 24 / 50 Choose the correct option 1 4 2 3 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 : 1/2 2/3 1/6 1/4 26 / 50 Choose the correct option: 1 None of these 2 3 27 / 50 Which of the following is an instance of non‐sampling error? Faulty selection of sample Detective frame All of these Bias due to interviewer 28 / 50 The vectors (a_{1}, a_{2}) and (b_{1}, b_{2}) in R^{(2)} are linearly dependent if and only if a_{1} b_{1}= a_{2 b2} a_{1} b_{2}= a_{2} b_{1} a_{1} a_{2}= b_{1} b_{2} a_{1}^{2} = b_{1}^{2} AND a_{2}^{2}=b_{2}^{2} 29 / 50 For any two events G and H, which of the following hold true? P(G∩H) ≥ P(G) ≥ P(G∪H) ≥ P(G)+P(H) P(G∩H) ≤ P(G∪H) ≤ P(G) ≤ P(G)+P(H) P(G∩H) ≤ P(G) ≤ P(G∪H) ≤ P(G)+P(H) P(G) + P(H) ≤ P(G) ≤ P(G∪H) ≤ P(G∩H) 30 / 50 The total yield of the treatments of a 22 factorial experiment replicated 4 times are: b0b1a02044a13252The simple effect of factor A at first level of B and the interaction effect AB can be estimated as 3 and ‐0.5 12 and ‐2 2.5 and ‐0.5 10 and ‐2 31 / 50 Let A_{1}, A_{2,} A_{3,} A_{4} be the events of answering the questions 1, 2, 3 and 4 respectively such that P(A_{1}) = 1/2, P(A_{2}) = 1/4, P(A_{3}) = 1/8, P(A_{4}) = 1/16, then P(A_{1} ∪A_{2} ∪ A_{3} ∪A_{4}) is: 1023/1024 1/1024 709/1024 4/511 32 / 50 Which of the following is NOT TRUE about Neyman‐Pearson Lemma in hypothesis testing? None of these The most powerful critical region is given by W = {x ∈ S; L_{0}/L_{1} >k}; where L_{0} and L_{1} are likelihood functions under H_{0} and H_{1} respectively, S is the sample space, and k is a positive constant. It does not give us the uniformly most powerful critical region It holds for only a simple null hypothesis against a simple alternative 33 / 50 Choose the correct option 3 1 None of these 2 34 / 50 Based on a random sample of size n (X_{1}, X_{2},…, X_{n}) from Cauchy(θ). A sufficient statistic for θ is Sufficient statistic does not exist for θ sample mean None of the above sample median 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: 95.8 and 11 95.8 and 12 57.5 and 12 57.5 and 11 36 / 50 An experimental design which allows an unequal number of observations for each treatment under study is Latin Square Design Completely Randomized Design Completely Randomized Block Design None of these 37 / 50 If X ~ U(0,1) then Y = -2log(X) will follow Gamma Exponential Log‐normal Chi‐square 38 / 50 Among the following system of equations2x‐5y+7z=6,x‐3y+4z=3,3x‐8y+11z=11,which one of the following is true? The system of equations are inconsistent x=1, y=3/5, z=1 is the solution None of these The system of equations are consistent 39 / 50 Choose the correct option: 1, 2 and 3 3 2 1 40 / 50 Choose the correct option 1 4 2 3 41 / 50 The set W={( a_{1}, a_{2}, a_{3}) : a_{1}, a_{2}, a_{3} ϵ R}, is not a subspace of R^{(3)} , if None of these a_{3}= a_{1}+ a_{2} a_{3}=0 a_{1}a_{2}=0 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(A^{c} ∪ B^{c} ) = 1/3 then P(A ∪ B^{c} ) is: 5/6 1/6 1/4 2/3 43 / 50 For Poisson distribution with parameter μ, the value of measure of Skewness and measure of Kurtosis are: μ and μ+ 3 1/3 and 1/μ + 3 1/μ and 1/μ 1/μ and 1/μ + 3 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: 1/26 7/13 3/52 8/13 45 / 50 Let X_{i}, i= 1, 2,…, n, be i.i.d random variables with E﴾X_{i}﴿=µ and var(X_{i}) < ∞. Consider an estimator T_{n} = 2* ∑^{n}_{i=1}iX_{i} /n(n+1), for estimating µ. Then, T_{n} is, Biased and not consistent Biased and consistent Unbiased but not consistent Unbiased and consistent 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 5/53 4/7 5/42 5/22 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: acd, cde, bce abc, bcde ade, bcde, abc ade, bcde 48 / 50 The arithmetic mean of two regression coefficient b_{XY} and b_{YX} is______ the correlation coefficient between X and Y. less than greater than equal to greater than less than equal to 49 / 50 While constructing a confidence interval for an unknown parameter using Pivotal quantity method, a pivotal quantity is defined as a function of a statistic T and the parameter θ, such that its distribution is independent of θ function of a statistic T, where T is sufficient for θ function of a statistic T, such that its distribution is a function of θ function of a statistic T, such that its distribution is independent of θ 50 / 50 Let X_{1}, X_{2},…, X_{n} be a random sample from U(‐θ, θ) distribution. Maximum likelihood estimator of θ is Minimum(‐X_{(1)}, X_{(n)}) X_{(n)}, the nth order statistic X_{(1)}, the first order statistic Maximum(‐X_{(1)}, X_{(n)}) Your score is 0% Restart quiz Testing Wrong shortcode initialized