ISS (Statistical Services) Statistics Paper I (New 2016 MCQ Pattern): Questions 385 - 387 of 471

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Question number: 385

» Probability » Kolmogorov's Inequalities

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MCQ▾

Question

Which of the following statement is correct?

Choices

Choice (4) Response

a.

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

b.

Kolmogorov’s Inequality is a special case of Martingale Maximal Inequality.

c.

None of the above

d.

Question does not provide sufficient data or is vague

Question number: 386

» Probability » Uniqueness and Continuity Theorems

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MCQ▾

Question

Let be random variables on such that,

Then, which of the following is correct?

Choices

Choice (4) Response

a.

is always increasing.

b.

does not converges for all .

c.

converges for all .

d.

None of the above

Question number: 387

» Probability » Kolmogorov's 0-1 Law

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Question

Consider an infinite random stream of fair coin tosses: an infinite sequence of 0′s and 1′s, chosen IID with equal probabilities at each step. Call the result of the coin toss (these variables generate the sample space). Which of the following is correct regarding the following limit?

Choices

Choice (4) Response

a.

According to Kolmogorov’s 0 - 1 law the limit never exist.

b.

According to Kolmogorov’s 0 - 1 law if there is no limit then it’s probability is 1.

c.

Strong law of large numbers states that the limit exists, with probability 0.

d.

Question does not provide sufficient data or is vague