ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 48 - 54 of 165

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Question number: 48

» Probability » Standard Probability Distributions » Geometric

Appeared in Year: 2010

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Let X have a geometric distribution, then for an two non-negative integers m and n,

Prove it

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Question number: 49

» Numerical Analysis » Numerical Integration

Appeared in Year: 2013

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Evaluate the following by taking seven ordinates of the integrand:

Explanation

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Question number: 50

» Probability » Standard Probability Distributions » Cauchy

Appeared in Year: 2011

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Obtain the median and the quartiles of the Cauchy distribution with p. d. f.

Explanation

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Question number: 51

» Numerical Analysis » Summation Formula » Euler-Maclaurin's

Appeared in Year: 2015

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By using Euler-Maclaurin formula, find the sum

Explanation

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Question number: 52

» Statistical Methods » Order Statistics » Maximum

Appeared in Year: 2014

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Let X 1, X 2, …, X n be n independently identically distributed random variables following an exponential distribution with mean parameter θ. Obtain the distributions of (i) Maximum (X 1, X 2, …, X n); (ii) Minimum (X 1, X 2, …, X n) and (iii) Median for n = 2m + 1, (m > 0)

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Question number: 53

» Probability » Characteristic Function

Appeared in Year: 2015

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Obtain the characteristic function of X whose pdf is

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Question number: 54

» Probability » Expectation

Appeared in Year: 2013

Essay Question▾

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Let X be a continuous random variable and have F (x) as the distribution function. If E [X] exists, then show that:

Explanation

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