Explanation Formula used: If the random variable X is uniformly distributed on the interval [ a , b ] , then the uniform probability density function is f ( x ) = { 1 b − a if a ≤ x ≤ b 0 otherwise . The respective cumulative distribution function is F ( x ) = { 0 if x < a x − a b − a if a ≤ x ≤ b 1 if x > b . Calculation: Given that X is uniformly distributed on [ 3 , 6 ] . Substitute a = 3 and b = 6 in the above formula to obtain probability density function. f ( x ) = { 1 6 − 3 if 3 ≤ x ≤ 6 0 otherwise = { 1 3 if 3 ≤ x ≤ 6 0 otherwise Thus, the probability density function f is f ( x ) = { 1 3 if 3 ≤ x ≤ 6 0 otherwise

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Chapter 11.4, Problem 2E

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To find: The probability density function f and the associated cumulative distribution function F for the uniformly distributed random variable X on [3,6].

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Chapter 11 Solutions

FIN 108 ISU LOOSE >IP<

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 probability density function f and the associated cumulative distribution function F for the uniformly distributed random variable X on [ 3 , 6 ] .

Solution Summary: The author explains the probability density function f and cumulative distribution function F for the uniformly distributed random variable X on left[3,6right].

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To find: The probability density function f and the associated cumulative distribution function F for the uniformly distributed random variable X on [3,6].

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Chapter 11 Solutions