ISS (Statistical Services) Statistics Paper I (New 2016 MCQ Pattern): Questions 384 - 387 of 472
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Question number: 384
» Probability » Moment and Probability Generating Functions
Question
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 number: 385
» Probability » Kolmogorov's Inequalities
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
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
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 | |