Explanation Definition used: If f is a probability density function, then the associated cumulative distribution function F is F ( x ) = P ( X ≤ x ) = ∫ − ∞ ∞ f ( t ) d t . Formula used: Let f ( x ) be the probability density function for a continuous random variable X . Median (m): “If m is the median, then m must satisfy P ( X ≤ m ) = 1 2 ”. Calculation: The given function is f ( x ) = { 2 e − 2 x if x ≥ 0 0 othewise . Use the definition of the cumulative distribution function to obtain F ( x ) as follows. For x < 0 , F ( x ) = P ( X < 0 ) = ∫ − ∞ x 0 d t [ ∵ f ( x ) = 0 for x < 0 ] = 0 Hence, the cumulative distribution function for x < 0 is F ( x ) = 0

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Author: Stocker

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Chapter 11.3, Problem 29E

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To find: The median for the given function.

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Chapter 11 Solutions

EBK CALCULUS FOR BUSINESS, ECONOMICS, L

Ch. 11.1 - Evaluate the following, if it converges: 3dx(x1)2.Ch. 11.1 - Prob. 2MP Ch. 11.1 - Prob. 3MP Ch. 11.1 - Prob. 4MP Ch. 11.1 - Prob. 5MP Ch. 11.1 - Prob. 6MP Ch. 11.1 - Prob. 1ED Ch. 11.1 - Prob. 2ED Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E

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The median for the given function.

Solution Summary: The author explains how to find the median for the given function. The median of the function is 0.347.

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