Explanation Given: The function in Problem 25 is given by f ( x ) = { 2 ( 1 + x ) 3 if x ≥ 0 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 ) = ∫ − ∞ x f ( t ) d t from the function f ( x ) = { 2 ( 1 + x ) 3 if x ≥ 0 0 otherwise as follows. For x < 0 , F ( x ) = ∫ − ∞ x f ( t ) d t = ∫ − ∞ x ( 0 ) d t = 0 For x ≥ 0 , F ( x ) = ∫ − ∞ x f ( t ) d t = ∫ − ∞ 0 f ( t ) d t + ∫ 0 x f ( t ) d t = ∫ − ∞ 0 ( 0 ) d t + ∫ 0 x 2 ( 1 + t ) 3 d t = ∫ 0 x 2 ( 1 + t ) − 3 d t After further simplification,

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Chapter 11.2, Problem 29E

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To find: The cumulative distribution function associated with the function in Problem 25 and then graph the respective function.

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Chapter 11.2, Problem 28E

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EP CALCULUS F/BUS.,ECON.-BRIEF-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 cumulative distribution function associated with the function in Problem 25 and then graph the respective function.

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