Explanation Given: The quartile points for a probability density function are the values x 1 , x 2 , x 3 that divide the area under the graph of the function into four equal parts. Definition used: Cumulative distribution functions : If f is a probability function and F ( x ) = ∫ − ∞ x f ( t ) d t is the associated cumulative distribution function. Calculation: The given function is f ( x ) = { 1 2 x if 0 ≤ x ≤ 2 0 othewise . If x < 0 , then F ( x ) = 0 . In the interval [ 0 , 2 ] , the value of F ( x ) is as follows. F ( x ) = ∫ − ∞ x f ( t ) d t = ∫ − ∞ 0 0 d t + ∫ 0 x 1 2 t d t = 1 2 [ t 2 2 ] 0 x = 1 2 [ x 2 2 − 0 2 2 ] = x 2 4 In case of x > 2 , the value of F ( x ) is as follows. F ( x ) = ∫ − ∞ x f ( t ) d t = ∫ − ∞ 0 0 d t + ∫ 0 2 1 2 t d t + ∫ 2 x 0 d t = 1 2 [ t 2 2 ] 0 2 = 1 2 [

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Chapter 11.3, Problem 37E

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To find: The quartile points for the probability density function f(x)={12x if 0≤x≤20 othewise.

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Chapter 11.3, Problem 36E

Chapter 11.3, Problem 38E

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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 quartile points for the probability density function f ( x ) = { 1 2 x if 0 ≤ x ≤ 2 0 othewise .

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To find: The quartile points for the probability density function f(x)={12x if 0≤x≤20 othewise.

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