Explanation Given: The function in Problem 26 is given by f ( x ) = { 2 ( 2 + x ) 2 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 ( 2 + x ) 2 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 ( 2 + t ) 2 d t = ∫ 0 x 2 ( 2 + t ) − 2 d t Simplify further,

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Chapter 11.2, Problem 30E

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To find: The cumulative distribution functions associated with the function in Problem 26 and then graph the respective function.

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Chapter 11.2, Problem 29E

Chapter 11.2, Problem 31E

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Chapter 11 Solutions

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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 cumulative distribution functions associated with the function in Problem 26 and then graph the respective function.

Solution Summary: The author explains how to find the cumulative distribution functions associated with the function in Problem 26 and graph the respective function.

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To find: The cumulative distribution functions associated with the function in Problem 26 and then graph the respective function.

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Chapter 11 Solutions