Probability-Probability Distributions (ISS Statistics Paper I (New 2016 MCQ Pattern)): Questions 51 - 54 of 109

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Question number: 51

» Probability » Probability Distributions » Multinomial

MCQ▾

Question

If X1,X2,,Xm are counts in cells/boxes 1 up to m, each box have different probability pi , and the fixed number of balls are n=x1+x2++xm . Then what is maximum Likelihood of Multinomial Cell Probabilities?

Choices

Choice (4) Response

a.

pi^=xi

b.

pi^=xin

c.

pi^=xin

d.

pi^=xi

Question number: 52

» Probability » Probability Distributions » Laplace

MCQ▾

Question

If (X1,X2,X3,X4) is a random sample of size 4 from a standard normal distribution. Then the U=X1X2+X3X4 will follow ________

Choices

Choice (4) Response

a.

Laplace distribution.

b.

Exponential distribution

c.

Bivariate normal distribution.

d.

Question does not provide sufficient data or is vague

Question number: 53

» Probability » Probability Distributions » Uniform

MCQ▾

Question

If X1,X2,,Xn are i. i. d. uniform on [0,θ] , then if X¯=i=1nXin . Then Var (X¯) is________.

Choices

Choice (4) Response

a.

θ26n2

b.

θ26n

c.

θ212n2

d.

None of the above

Question number: 54

» Probability » Probability Distributions » Negative Binomial

MCQ▾

Question

In a sequence of independent Bernoulli (p) trails, if X denotes the number of failures before rth (fixed) success, then the expected value of X will be ________

Choices

Choice (4) Response

a.

r(1p)p2

b.

rp(1p)

c.

r(1p)p

d.

Question does not provide sufficient data or is vague

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