# Probability-Modes of Convergences of Sequences of Random Variables [ISS (Statistical Services) Statistics Paper I (New 2016 MCQ Pattern)]: Questions 1 - 3 of 11

Access detailed explanations (illustrated with images and videos) to **472** questions. Access all new questions we will add tracking exam-pattern and syllabus changes. *Unlimited Access for Unlimited Time*!

View Sample Explanation or View Features.

Rs. 300.00 or

How to register?

## Question number: 1

» Probability » Modes of Convergences of Sequences of Random Variables » In Distribution

### Question

Suppose that has the discrete uniform distribution on for each and let denote the probability density function of Let have the continuous uniform distribution on the interval . Then which of the following is correct option?

### Choices

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

a. | as for all | |

b. | for each but | |

c. | The distribution of converges to the distribution of as | |

d. | All a. , b. and c. are correct |

## Question number: 2

» Probability » Modes of Convergences of Sequences of Random Variables » In Distribution

### Question

Suppose that is a sequence of random variables (defined on the same probability space) and that the distribution of converges to the distribution of the constant . Then________.

### Choices

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

a. | as -th mean | |

b. | as in probability | |

c. | almost everywhere | |

d. | None of the above |

## Question number: 3

» Probability » Modes of Convergences of Sequences of Random Variables » In Distribution

### Question

Consider a random permutation of the elements in the set . We say that s match occurs at position . If denotes the number of matches, then the distribution of converges to ________ as .

### Choices

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

a. | Exponential distribution with parameter 1 | |

b. | Laplace distribution with location parameter 0 and scale parameter 1 | |

c. | Poisson distribution with parameter 1 | |

d. | None of the above |