ISS (Statistical Services) Statistics Paper I (New 2016 MCQ Pattern): Questions 397 - 399 of 469

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Question number: 397

» Probability » Kolmogorov's 0-1 Law

MCQ▾

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 Equation coin toss Equation (these variables generate the sample space). Which of the following is correct regarding the following limit?

Equation

Choices

Choice (4) Response

a.

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

b.

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

c.

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

d.

Question does not provide sufficient data or is vague

Question number: 398

» Probability » Laws of Large Numbers

MCQ▾

Question

Let Equation be a sequence of independent, identically distributed random variables, each having finite mean Equation . Then for any Equation , which of the following option is/are correct according to statement of Weak law of large number?

Choices

Choice (4) Response

a.

Equation

b.

Equation

c.

Question does not provide sufficient data or is vague

d.

All of the above

Question number: 399

» Probability » Kolmogorov's Inequalities

MCQ▾

Question

For an infinite sequenceEquation , for every Equation where Equation Equation be independent random variables on a common probability spaceEquation with expected value Equation and variance Equation for Equation . and Equation which of the following inequality holds?

Choices

Choice (4) Response

a.

Equation

b.

Equation

c.

Equation

d.

Equation

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