Probability-Kolmogorov's Inequalities (ISS Statistics Paper I (New 2016 MCQ Pattern)): Questions 1 - 3 of 5

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Question number: 1

» 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: 2

» 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

Question number: 3

» Probability » Kolmogorov's Inequalities

MCQ▾

Question

Which of the following statement is correct?

Choices

Choice (4) Response
a.

Chebyshev’s Inequality is an special case of Kroneckers lemma.

b.

Chebyshev’s Inequality is an special case of Kolmogorov’s Inequality.

c. Question does not provide sufficient data or is vague
d. None of the above

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