# ISS (Statistical Services) Statistics Paper I (New 2016 MCQ Pattern): Questions 384 - 387 of 472

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## Question 384

### Question

MCQ▾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 385

### Question

MCQ▾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 386

### Question

MCQ▾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 387

### Question

MCQ▾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 |