ISS (Statistical Services) Statistics Paper I (New 2016 MCQ Pattern): Questions 372 - 375 of 472
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Question 372
Question
MCQ▾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 373
Question
MCQ▾If is the number of points rolled with a balanced die, find the expected value of .
Choices
Choice (4) | Response | |
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a. | ||
b. | ||
c. | ||
d. | None of the above |
Question 374
Question
MCQ▾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 | |
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a. | ||
b. | ||
c. | ||
d. | None of the above |
Question 375
Question
MCQ▾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 |