# Probability (ISS Statistics Paper I (New 2016 MCQ Pattern)): Questions 195 - 198 of 205

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## Question number: 195

» Probability » Moment and Probability Generating Functions

### Question

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. | All of the above |

## Question number: 196

» 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. | |

b. | Kolmogorov’s Inequality is a special case of Chebyshev’s Inequality. | |

c. | All of the above | |

d. | None of the above |

## Question number: 197

» 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 . | |

b. | does not converges for all . | |

c. | is always increasing. | |

d. | None of the above |

## Question number: 198

» 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. | |

b. | According to Kolmogorov’s 0 - 1 law the limit never exist. | |

c. | According to Kolmogorov’s 0 - 1 law if there is no limit then it’s probability is 1. | |

d. | Question does not provide sufficient data or is vague |