# ISS (Statistical Services) Statistics Paper II (New 2016 MCQ Pattern): Questions 39 - 43 of 253

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## Question 39

### Question

MCQ▾If are random observations on a Bernoulli variate X taking the value 1 with probability and the value 0 with the probability then is a Consistent estimator of . This statement is

### Choices

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

a. | True | |

b. | False | |

c. | Since is not a consistent estimator of , this is false. | |

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

## Question 40

### Question

MCQ▾Let be a random sample of size n = 3 from a distribution with mean and variance . Then is a unbiased estimator of

### Choices

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

a. | ||

b. | ||

c. | ||

d. | None of the above |

## Question 41

### Question

MCQ▾An estimator is said to be sufficient for a parameter, if it contains

### Choices

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

a. | If the conditional distribution of , given T is independent of the parameter. | |

b. | All the information in the sample regarding the parameter. | |

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

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

## Question 42

### Question

MCQ▾A random sample of size 5 is drawn from a normal population with unknown mean . Then is a unbiased estimator of

### Choices

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

a. | ||

b. | ||

c. | ||

d. |

## Question 43

### Question

MCQ▾If , then which of the following is true?

### Choices

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

a. | is a biased estimator of | |

b. | ||

c. | is a Unbiased estimator | |

d. | None of the above |