# Probability (ISS Statistics Paper I (New 2016 MCQ Pattern)): Questions 147 - 150 of 205

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## Question number: 147

» Probability » Probability Distributions » Joint and Marginal Distributions

### Question

Continuous random variables and have a joint distribution with density function for and . Find

### Choices

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

a. |
| |

b. |
| |

c. |
| |

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

## Question number: 148

» Probability » Probability Distributions » Gamma

### Question

A chi-square (with degree of freedom) probability density function satisfies which of the following property/properties?

### Choices

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

a. | If then is decreasing with | |

b. | If , then is concave downward. | |

c. | If , is increasing with as . | |

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

## Question number: 149

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

### Question

Suppose that is a sequence of independent random variables with , ; , then the following option is correct?

### Choices

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

a. | almost everywhere | |

b. | as | |

c. | in probability | |

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

## Question number: 150

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

### Question

Consider the following statements and then choose the option in which the given statements are equivalent.

I)

II)

III) for every

IV) for every

V) for every

### Choices

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

a. | II and IV | |

b. | I, III, V | |

c. | I, V | |

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