# Statistical Methods-Order Statistics (ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)): Questions 1 - 1 of 1

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## Question number: 1

» Statistical Methods » Order Statistics » Maximum

Appeared in Year: 2014

### Describe in Detail

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)

### Explanation

Let X _{1}, X _{2}, …, X _{n}, be n independently identically distributed random variables following an exponential distribution with mean parameter θ. The probability density and distribution function is

Let X _{ (1) }, X _{ (2) }, …, X _{ (n) } denote the order statistic of