ISS (Statistical Services) Statistics Paper I (New 2016 MCQ Pattern): Questions 386 - 388 of 471
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Question number: 386
» 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 Martingale Maximal Inequality. |
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| b. | Kolmogorov’s Inequality is a special case of Chebyshev’s Inequality. |
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| c. | All of the above |
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| d. | None of the above |
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Question number: 387
» 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. | converges for all . |
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| b. | does not converges for all . |
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| c. | is always increasing. |
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| d. | None of the above |
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Question number: 388
» 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. | Strong law of large numbers states that the limit exists, with probability 0. |
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| b. | According to Kolmogorov’s 0 - 1 law the limit never exist. |
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| c. | According to Kolmogorov’s 0 - 1 law if there is no limit then it’s probability is 1. |
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| d. | Question does not provide sufficient data or is vague |
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