Explanation Formula used: Let f ( x ) be the probability density function for a continuous random variable X . ∫ − ∞ ∞ f ( x ) d x = 1 (1) Expected value or mean ( µ ): μ = ∫ − ∞ ∞ x f ( x ) d x (2) Variance: V ( x ) = ∫ − ∞ ∞ x 2 f ( x ) − μ 2 (3) Standard deviation ( σ ): σ = v ( x ) (4) Calculation: Compute ∫ − ∞ ∞ ( a x 2 + b x + c ) f ( x ) d x as follows. ∫ − ∞ ∞ ( a x 2 + b x + c ) f ( x ) d x = ∫ − ∞ ∞ a x 2 f ( x ) d x + ∫ − ∞ ∞ b x f ( x ) d x + ∫ − ∞ ∞ c f ( x ) d x = a ∫ − ∞ ∞ x 2 f ( x ) d x + b ∫ − ∞ ∞ x f ( x ) d x + c ∫ − ∞ ∞ f ( x ) d x Thus, ∫ − ∞ ∞ ( a x 2 + b x + c ) f ( x ) d x = a ∫ − ∞ ∞ x 2 f ( x ) d x + b ∫ − ∞ ∞ x f ( x ) d x + c ∫ − ∞ ∞ f ( x ) d x

Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.

15th Edition

ISBN: 9781323047620

Author: Barnett, Ziegler, Byleen

Publisher: Pearson Education

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Chapter 11, Problem 32RE

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Chapter 11, Problem 31RE

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Chapter 11 Solutions

Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.

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 given integral and express the result in terms of μ , σ , a , b and c .

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To evaluate: The given integral and express the result in terms of μ,σ,a,b and c.

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Chapter 11 Solutions