Explanation Definition used: Median: It is the value of the random variable and which divides the area under the graph of the probability density function into 2 equal parts. If m satisfy the condition P ( X ≤ m ) = 1 2 , then m is the median. Calculation: The given function is f ( x ) = { 1 2 x 2 + 3 2 x 4 if x ≥ 1 0 Otherwise . Initially consider the case when x < 0 . Use the definition of the cumulative distribution function as, 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 . Obtain cumulative distribution function when x ≥ 1 as, F ( x ) = P ( X ≤ x ) = ∫ − ∞ x f ( t ) d t = ∫ − ∞ 1 0 d t + ∫ 1 x ( 1 2 t 2 + 3 2 t 4 ) d t On further simplification, F ( x ) = ( − t − 1 2 − t − 3 2 ) 1 x =

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Chapter 11.3, Problem 43E

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To find: The median of the probability density function f(x)={12x2+32x4 if x≥10 Otherwise .

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Chapter 11.3, Problem 42E

Chapter 11.3, Problem 44E

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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 of the probability density function f ( x ) = { 1 2 x 2 + 3 2 x 4 if x ≥ 1 0 Otherwise .

Solution Summary: The author calculates the median of the probability density function f(x)=l12x

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To find: The median of the probability density function f(x)={12x2+32x4 if x≥10 Otherwise .

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Chapter 11 Solutions