MCQs Statistics and Probabulity PDF

SPT- MCQ question bank 1.If 𝑃(𝐴) = 1⁄4 , 𝑃(𝐵) = 1⁄3 , 𝑃(𝐴 ∪ 𝐵) = 1⁄2 then 𝑃(𝐴|𝐵) is ______________ a)1⁄12 b)1⁄3 c)1⁄4 d)1⁄6 2. Probability of an impossible event is (a) Zero (b) 1 (c) 1/4 (d) ½ 3.The pdf of random variable X is 𝑓(𝑥)...

SPT- MCQ question bank 1.If 𝑃(𝐴) = 1⁄4 , 𝑃(𝐵) = 1⁄3 , 𝑃(𝐴 ∪ 𝐵) = 1⁄2 then 𝑃(𝐴|𝐵) is ______________ a)1⁄12 b)1⁄3 c)1⁄4 d)1⁄6 2. Probability of an impossible event is (a) Zero (b) 1 (c) 1/4 (d) ½ 3.The pdf of random variable X is 𝑓(𝑥) = 𝑘𝑥 , 0 < 𝑥 < 1 then 𝑘 is--------------- a)0 b)1 c)2 d)3 4. If X is a discrete random variable with (𝑥, 𝑝(𝑥)) values as (0, 𝑘), (1,2𝑘), (2,3𝑘), (3,4𝑘) ,then value of k is____ a) 0.4 b) 0.1 c)1 d)10 5.If 𝑃(𝐴) = 0.4, 𝑃(𝐵) = 0.04 , 𝑃(𝐴  𝐵) = 0.01 then 𝑃(𝐴| B ) = ______________ a)0.05 b) 0.40625 c) 0.593 d) 0.64  A 6. If A and B are mutually exclusive events then P  is_________ B a)0 b) S c)∅ d)1  A 7. If A and B are independent events then P  = _________ B a)P(A) b) P(B) c)𝑃(𝐴 ∩ 𝐵) d)1 8. If X is a discrete random variable with V(X)=7.15 then V(19-4X)= a) 114.4 b)-9.6 c)-95.4 d)7.2 9.If 𝐸[𝑋] = 3 , 𝐸[𝑋 2 ] = 10 then 𝑉(𝑋) is ___________ a)1 b)7 c)97 d)0 10.If 𝐸[𝑋] = 2 , 𝐸[𝑋 2 ] = 12 then standard deviation is ___________ a)8 b)2.8284 c)0.2828 d)3.1622 11.If 𝑉(𝑋) = 15 then 𝑉(8𝑋) is ___________  a)30.9838 b)10.9544 c)120 d)960 12.If A and B are mutually exclusive events then 𝑃(𝐴 ∩ 𝐵) is_________ a)0 b) S c)∅ d)1 13.If 𝐸[𝑋] = 3 , 𝑉[𝑋] = 18 then 𝐸(𝑋 2 ) is ___________ a) 9 b)27 c)21 d)15 14.The pdf of random variable is 2𝑥 , 0 < 𝑥 < 1 then 𝑃(0 < 𝑋 < 0.5) is____________ a) 0.125 b)0.5 c)0.25 d)1 15.If (𝑥, 𝑝(𝑥)) values are (0,0.5), (1,0.2), (2,0.1), (3,0.2) then 𝑃(0 < 𝑋 < 2) is______ a) 0.8 b)0.3 c) 0.7 d) 0.2 16.If X and Y are independent random variable then E(XY)=_______ a)E(X+Y) b)E(X)E(Y) c)E(X-Y) d)0 17.If marginal distribution of X is (0,0.4), (1,0.2), (2,0.1), (3,0.3) then E(X) is__________________ a)1 b)1.3 c)1.7 d)3.3 18. If X and Y are independent random variable then V ( X − Y ) = a) V ( X ) + V (Y ) b) V ( X ) − V (Y ) c) V ( X )V (Y ) d)none of these 19. If X and Y are independent random variables with variances of X and Y are respectively 1 and 2, Then V[2X-3Y]=_______________ (a)8 (b) -14 (c) 22 (d) 0 20. If marginal distribution of X is (0, 0.4), (1, 0.2), (2, 0.1), (3, 0.3) then E(X2) is__________________ a)1 b)1.3 c)1.7 d)3.3 21. If 𝑃(𝐴) = 0.4 , 𝑃(𝐵) = 0.04 , 𝑃(𝐴 ∩ 𝐵) = 0.01 then P ( A | B ) = ______________ a)0.05 b)0.25 c)0.59375 d)0.64 22. E ( X − E ( X )) = a) V ( X ) b) E ( X ) c) 0 d) E ( X ) − X 23. If the joint pdf of X is f ( x, y ) = e − ( x + y ) , 0  x, y   then the marginal distribution of X is −x −x −y b) − e x a) e c) e d) e 24. If X and Y are random variables with a and b constants, then Cov(aX, bY)=________ a) (a+b)Cov(X,Y) b) a2Cov (X)+ b2Cov(Y) c) abCov(X,Y) d) V(aX+bY) 25.If X and Y are independent random variables, then Cov(X,Y) is ____ a) -1 b) 0 c) 1 d) 26.The mean of binomial distribution is a)𝑛𝑝 b)𝑛𝑞 c)𝑛𝑝𝑞 d)√𝑛𝑝𝑞 27. The pdf of standard normal distribution is symmetric about _______ ( a) y-axis (b)x- axis ( c) the line x =  (d) both (a) and (b) 28. In binomial distribution if n=10 and p=0.1 then standard deviation is __________ a) 9 b)0.9486 c)0.9 d)1 29. The variance of binomial distribution is a)𝑛𝑝 b)𝑛𝑞 c)𝑛𝑝𝑞 d)√𝑛𝑝𝑞 30.If p is a probability of success and q is a probability of failure then (𝑝 + 𝑞)5 is a)1 b)0 c)0.5 d)2𝑛 31.The standard deviation of binomial distribution is a)𝑛𝑝 b)𝑛𝑞 c)𝑛𝑝𝑞 d)√𝑛𝑝𝑞 32.If 6 coins are tossed then probability of getting exactly 3 heads is a)0.2325 b)0.3125 c)0.2135 d)0.3852 33.The probability function for poisson distribution is 𝑥 𝑥 𝑥 λ 𝑒 −λ 𝑥! λ λ 𝑒λ a) b)𝑥 c) d) 𝑥! λ 𝑒 −λ 𝑥!𝑒 −λ 𝑥! 34.The probability function for binomial distribution is a)𝑛𝐶𝑥 𝑝 𝑥 𝑞𝑛+𝑥 b) 𝑛𝐶𝑥 𝑝 𝑥 𝑞𝑛−𝑥 c)𝑛𝐶𝑥 𝑝 𝑥 𝑞𝑛 d)𝑛𝐶𝑥 𝑝 𝑥 𝑞 𝑥 35. Probability distribution which is the limiting case of binomial distribution is ___________ a)Poisson distribution b)exponential distribution c)normal distribution d)both a and c 36.For standard normal distribution, standard deviation is __________ a)0 b)1 c)0.5 d)0.25 37.For standard normal distribution mean is __________ a)0 b)1 c)0.5 d)0.25 38. In Poisson distribution if n=10000 and p=0.001 then standard deviation is __________ a) 10 b)3.1622 c)2.8284 d)3.4641 39.In exponential distribution if 𝛼 = 1⁄3 then mean is ______ a)3 b)1⁄3 c)√3 d)1⁄ √3 40.In exponential distribution if 𝛼 = 1⁄2 then variance is ______ a)√4 b)1⁄4 c)4 d)1⁄ √4 41.The variance of poisson distribution with parameter λ=2 is _________ a)4 b)0.5 c)1.4142 d)2 42. In a Poisson distribution if 2𝑃(𝑋 = 1) = 𝑃(𝑋 = 2) the variance is a)0 b)-1 c)4 d)2 43.In a Poisson distribution if 𝑃(𝑋 = 2) = 𝑃(𝑋 = 3) then𝑃(𝑋 = 0) is ____________ a)𝑒 3 b)𝑒 −3 c)𝑒 1 𝑑)𝑒 −1 44. Which of the following is not a characteristic of the binomial distribution? a) There is a sequence of identical trials b) Each trial results in two or more outcomes c) The trials are independent of each other c) Probability of success is same from one trial to  another. 45. If  is the mean of Poisson distribution then P ( X = 0) is given by −  a) e b) e c) e d) 0 47. If a random variable X satisfies the Poisson distribution with a mean value of 2 then P( X  1) is −2 −2 a) 1 − e b) 1 − e c) 1 + e d) 1 + e 2 2 48. Which of the following statement is correct? a) The mean of the Poisson distribution (with parameter  ) equals the mean of the exponential distribution (with parameter  ) only when  =  = 1. b) The exponential distribution is continuous and defined over the interval (− ,  ). c) The binomial distribution has equal mean and variance only when p=0.5. d) All the above. X 49. If X is a normal variate and = Y + 6 where Y has N (0,1) then mean and variance of X are 2 a) 6, 2 b)12, 4 c)6,4 d)12, 2 50. Suppose X ~ N(5, 32). What is P(X