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 | |