# Probability-Probability Distributions (ISS Statistics Paper I (New 2016 MCQ Pattern)): Questions 103 - 106 of 109

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## Question number: 103

» 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 | |
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a. |
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b. |
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c. |
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d. | Question does not provide sufficient data or is vague |

## Question number: 104

» 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: 105

» Probability » Probability Distributions » Beta

### Question

If has the distribution with degrees of freedom in the numerator and degrees of freedom in the denominator then, will follow ________ distribution.

### Choices

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

a. |
| |

b. | with degrees of freedom. | |

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

## Question number: 106

» Probability » Probability Distributions » Distributions of Functions of Random Variables

### Question

Suppose and are independent exponential random variables with parameter . If . Then the marginal distribution of or will follow ________.

### Choices

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

a. | Exponential distribution with parameter | |

b. | Poisson distribution with parameter | |

c. | Exponential distribution with parameter | |

d. | None of the above |