(a) Explanation Given: The function f ( x ) = x 8 − 1 4 is a probability density function for [ 2 , 6 ] . Definition used: Median : If X is a continuous random variable with probability function f on [ a , b ] , then the median of X is the number m such that ∫ a m f ( x ) d x = 1 2 . Calculation: Consider the given function f ( x ) = x 8 − 1 4 for [ 2 , 6 ] . Use the above mentioned definition and find median, ∫ 2 m ( x 8 − 1 4 ) d x = 1 2 ( ∵ a = 2 ) Evaluate the integral on the left, ∫ 2 m ( x 8 − 1 4 ) d x = 1 8 [ x 2 2 ] 2 m − 1 4 [ x ] 2 m = 1 16 [ m 2 − 2 2 ] − 1 4 [ m − 2 ] = 1 16 [ m 2 − 4 ] − 1 4 [ m − 2 ] Set this equal to 1 2 (b) To determine To find: The probability that the random variable is between the expected value and the median.

11th Edition

ISBN: 2818440028625

Author: Lial

Publisher: ELSEVIER

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Chapter 11.2, Problem 17E

(a)

To determine

To compute: The median.

(b)

To determine

To find: The probability that the random variable is between the expected value and the median.

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Chapter 11.2, Problem 16E

Chapter 11.2, Problem 18E

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