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 ) = { 4 ( 2 + x ) 2 if 0 ≤ x ≤ 2 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 . For 0 ≤ x < 2 , F ( x ) = P ( X ≤ x ) = ∫ − ∞ x f ( t ) d t = ∫ − ∞ 0 0 d t + ∫ 0 x ( 4 ( 2 + t ) 2 ) d t On further simplification, F ( x ) = ∫ 0 x ( 4 ( 2 + t ) 2 ) d t = ( − 4 2 + t ) 0 x = − 4 2 + x − − 4 2 + 0 = − 4 2 + x + 2 So, the cumulative distribution function for 0 ≤ x < 2 is F ( x ) = − 4 2 + x + 2

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Chapter 11.3, Problem 25E

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To find: The median for the given function.

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Chapter 11 Solutions

EP CALCULUS FOR BUSINESS..-MYLAB ACCESS

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 that the median for the given function is 23.

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