ISS (Statistical Services) Statistics Paper I (New 2016 MCQ Pattern): Questions 374 - 378 of 472
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Question number: 374
» Probability » Mathematical Expectation and Conditional Expectation
Question
If is the number of points rolled with a balanced die, find the expected value of .
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| d. | None of the above |
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Question number: 375
» Probability » Moment and Probability Generating Functions
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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 .
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| d. | None of the above |
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Question number: 376
» 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?
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| Choice (4) | Response | |
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| a. | There always exist finite connected component. |
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| b. | Existence of an infinite connected component is impossible. |
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| c. | Probability that there exists an infinite connected component is 0.5. |
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| d. | None of the above |
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Question number: 377
» Probability » Mathematical Expectation and Conditional Expectation
Question
Let be an exponential random variable with parameter . It’s characteristic function is________.
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| d. | Question does not provide sufficient data or is vague |
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Question number: 378
» Probability » Central Limit Theorems for Independent Variables
Question
Suppose that you have a sample of values from a population with mean and standard deviation. What is the probability that the sample mean will be in the interval ?
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| Choice (4) | Response | |
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| a. | 0.1056 |
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| b. | 0.8944 |
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| c. | 0.7888 |
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| d. | 0.2112 |
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