ISS (Statistical Services) Statistics Paper I (New 2016 MCQ Pattern): Questions 384 - 387 of 472

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Question 384

Question

MCQ▾

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

Choices

Choice (4)Response

a.

b.

c.

d.

None of the above

Question 385

Question

MCQ▾

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 386

Question

MCQ▾

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 387

Question

MCQ▾

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