Explanation Definition used: If f is a probability density function, then the associated cumulative distribution function F is defined by F ( x ) = P ( X ≤ x ) = ∫ − ∞ x f ( t ) d t . Calculation: From problem 17, the probability density function is f ( x ) = { 1 2 e − x 2 if x ≥ 0 0 otherwise . Initially consider the case of x < 0 . Use the definition of the cumulative distribution function to obtain F ( x ) . F ( x ) = P ( X < 0 ) = ∫ − ∞ 0 0 d t = 0 Thus, the cumulative distribution function when x < 0 is F ( x ) = 0 . In the same manner for x ≥ 0 , compute F ( x ) . F ( x ) = P ( X ≤ x ) = ∫ − ∞ x f ( t ) d t = ∫ − ∞ 0 f ( t ) d t + ∫ 0 x f ( t ) d

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Chapter 11, Problem 19RE

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Chapter 11 Solutions

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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