Explanation Given: The function is f ( x ) = { 1 2 + 1 2 x 3 if − 1 ≤ x ≤ 1 0 otherwise . Definition: Cumulative Distribution Function : “If f is a probability density function, then the associated cumulative function F is defined by F ( x ) = P ( X ≤ x ) = ∫ − ∞ x f ( t ) d t ”. Calculation: Obtain F ( x ) from the function f ( x ) = { 1 2 + 1 2 x 3 if − 1 ≤ x ≤ 1 0 otherwise by using above definition. For x < − 1 , F ( x ) = ∫ − ∞ x f ( t ) d t = ∫ − ∞ x ( 0 ) d t = 0 For − 1 ≤ x ≤ 1 , F ( x ) = ∫ − ∞ x f ( t ) d t = ∫ − ∞ − 1 f ( t ) d t + ∫ − 1 x f ( t ) d t = ∫ − ∞ − 1 ( 0 ) d t + ∫ − 1 x ( 1 2 + 1 2 t 3 ) d t = ∫ − 1 x ( 1 2 t + 1 2 ⋅ t 4 4 ) d t Further simplification, F ( x ) = [ 1 2 ⋅ t + t 4 8 ] − 1 x = [ x 2 + x 4 8 − ( − 1 4 − 1 8 ) ] = x 2 + x 3 8 + 2 + 1 8 = 3 8 + 1 2 x + 1 8 x 4 For x ≥ 1 , F ( x ) = ∫ − ∞ x f ( t ) d t = ∫ − ∞ − 1 f ( t ) d t + ∫ − 1 1 f ( t ) d t +

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Chapter 11.2, Problem 35E

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To find: The cumulative distribution function and then graph that function and given function.

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Chapter 11.2, Problem 34E

Chapter 11.2, Problem 36E

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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 cumulative distribution function and then graph that function and given function.

Solution Summary: The author explains how to find the cumulative distribution function and graph it. If f is a probability density function, the associated cumulative function F is defined.

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To find: The cumulative distribution function and then graph that function and given function.

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Chapter 11 Solutions