Probability (ISS Statistics Paper I (New 2016 MCQ Pattern)): Questions 158 - 160 of 205

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Question number: 158

» Probability » Moment and Probability Generating Functions

MCQ▾

Question

For a random variable X , if we have the moment generating function MX(s)=22s , for s(2, 2) . Then the distribution of X is ________.

Choices

Choice (4) Response

a.

X~Exponential(2)

b.

X~Normal(0, 2)

c.

X~Poission(2)

d.

Question does not provide sufficient data or is vague

Question number: 159

» Probability » Kolmogorov's Inequalities

MCQ▾

Question

For every n and every c>0, if X1,,Xn:ΩR be independent random variables on a common probability space (Ω,F,P), with expected value E[Xk]=0 and variance Var[Xk]<+ for k=1,,n . and Sk=X1++Xn which of the following inequality holds?

Choices

Choice (4) Response

a.

P(max1kn+1 Sk c)1c2E(Sn2)

b.

P(max1kn Sk c)1c2E(Sn)

c.

P(max1kn Sk c)1c2E(Sn2)

d.

P(max1kn Sk c2)1c2E(Sn)

Question number: 160

» Probability » Kolmogorov's Inequalities

MCQ▾

Question

Which of the following is/are correct regarding statement of Kolmogorov’s Inequalities?

Choices

Choice (4) Response

a.

Random variables involved share common probability space.

b.

Expected value of all random variable is 0.

c.

The random variables involved are independent.

d.

All a. , b. and c. are correct

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