# ISS (Statistical Services) Statistics Paper I (New 2016 MCQ Pattern): Questions 372 - 375 of 472

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## Question 372

### Question

MCQ▾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 373

### Question

MCQ▾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 374

### Question

MCQ▾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 375

### Question

MCQ▾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 |