# ISS (Statistical Services) Statistics Paper I (New 2016 MCQ Pattern): Questions 371 - 375 of 472

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## Question number: 371

### Question

Suppose are independent events with where . If then, which of the following is correct?

### Choices

Choice (4) | Response | |
---|---|---|

a. | a. s | |

b. | a. s | |

c. | does not converge. | |

d. | in probability. |

## Question number: 372

### Question

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 number: 373

» Probability » Mathematical Expectation and Conditional Expectation

### Question

If is the number of points rolled with a balanced die, find the expected value of .

### Choices

Choice (4) | Response | |
---|---|---|

a. |
| |

b. |
| |

c. |
| |

d. | None of the above |

## Question number: 374

» Probability » Moment and Probability Generating Functions

### Question

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 | |
---|---|---|

a. |
| |

b. |
| |

c. |
| |

d. | None of the above |

## Question number: 375

» 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?

### 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 |