# Probability-Modes of Convergences of Sequences of Random Variables (ISS Statistics Paper I (New 2016 MCQ Pattern)): Questions 4 - 7 of 11

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## Question number: 4

» Probability » Modes of Convergences of Sequences of Random Variables » With Probability One

### Question

If as with probability 1 then,

### Choices

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

a. | as in probability. | |

b. | as in r-th mean. | |

c. | as almost everywhere. | |

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

## Question number: 5

» Probability » Modes of Convergences of Sequences of Random Variables » In Mean Square

### Question

If in mean, then ________.

### Choices

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

a. | almost everywhere | |

b. | in distribution. | |

c. | in probability. | |

d. | Both b. and c. are correct |

## Question number: 6

» Probability » Modes of Convergences of Sequences of Random Variables » In Mean Square

### Question

If then in the -th mean implies ________.

### Choices

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

a. | in -th mean. | |

b. | in -th mean. | |

c. | almost everywhere. | |

d. | All of the above |

## Question number: 7

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

### Question

Consider the following events and then choose the option in which the given events are same.

I) does not converges to as .

II) converges to as

III) For some for infinitely many

IV) For some for infinitely many .

### Choices

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

a. | I and III | |

b. | II and III | |

c. | II and IV | |

d. | None of the above |