ISS (Statistical Services) Statistics Paper I (New 2016 MCQ Pattern): Questions 371 - 375 of 472
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Question number: 371
Question
Suppose are independent events with where . If then, which of the following is correct?
Choices
| Choice (4) | Response | |
|---|---|---|
a. | a. s | |
b. | a. s | |
c. | does not converge. | |
d. | in probability. | |
Question number: 372
Question
Let be independent and equidistributed. Then which of the following is correct regarding ?
Choices
| Choice (4) | Response | |
|---|---|---|
a. | If are infinite then will be larger than infinitely many times with probability 0. | |
b. | If are finite then will be larger than infinitely many times with probability 1. | |
c. | None of the above | |
d. | Question does not provide sufficient data or is vague | |
Question number: 373
» Probability » Mathematical Expectation and Conditional Expectation
Question
If is the number of points rolled with a balanced die, find the expected value of .
Choices
| Choice (4) | Response | |
|---|---|---|
a. |
| |
b. |
| |
c. |
| |
d. | None of the above | |
Question number: 374
» Probability » Moment and Probability Generating Functions
Question
Suppose that and are independent random variables taking values in N, with probability generating functions and having radii of convergence and , respectively. Then the probability generating function of is given by________ for .
Choices
| Choice (4) | Response | |
|---|---|---|
a. |
| |
b. |
| |
c. |
| |
d. | None of the above | |
Question number: 375
» Probability » Kolmogorov's 0-1 Law
Question
Consider the random graph we get from the square grid by keeping each edge with probability p (0 < p < 1 some predetermined constant) IID, and deleting it otherwise (this is percolation on the square grid, and has been extensively studied). Which of the following is correct regarding an infinite connected component somewhere in the graph?
Choices
| Choice (4) | Response | |
|---|---|---|
a. | There always exist finite connected component. | |
b. | Existence of an infinite connected component is impossible. | |
c. | Probability that there exists an infinite connected component is 0.5. | |
d. | None of the above | |