ISS Statistics Paper I (New 2016 MCQ Pattern): Questions 394 - 397 of 454

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Question number: 394

» Probability » Moment and Probability Generating Functions

MCQ▾

Question

Suppose that N is a random variable taking values in N. The probability generating function P of N will satisfy the following properties.

Choices

Choice (4) Response

a.

P(Niseven)=12[P(1)P(1)]

b.

P(Niseven)=12[1+P(1)]

c.

P(Niseven)=12[1P(1)]

d.

All of the above

Question number: 395

» Probability » Kolmogorov's Inequalities

MCQ▾

Question

Which of the following statement is correct?

Choices

Choice (4) Response

a.

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

b.

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

c.

All of the above

d.

None of the above

Question number: 396

» Probability » Uniqueness and Continuity Theorems

MCQ▾

Question

Let Xn,X be random variables on (Ω,F,P) such that,

limnXn(t)X(t),tR Then, which of the following is correct?

Choices

Choice (4) Response

a.

FXn(x) converges for all xR .

b.

FXn(x) does not converges for all xR .

c.

FXn(x) is always increasing.

d.

None of the above

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

limn(X1++Xn)n

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

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