Explanation Given: The probability density function is f ( x ) = 1 10 e − x / 10 , ( 0 ≤ x ≤ ∞ ) . It is described the successive arrivals of planes at the Carson Airport. Formula used: “Consider the probability density function f defined in the interval [ a , b ] associated with the continuous random variable X . The expected value of X is E ( X ) = ∫ a b x f ( x ) d x ”. Integration by parts, ∫ u d v = u v − ∫ v d u . Calculation: Obtaining the expected time taken, to see the arrive of another plane same as find the expect value of f ( x ) . Consider the density function f ( x ) = 1 10 e − x / 10 , ( 0 ≤ x ≤ ∞ ) . The expected value of X of the above function can be calculate as follows, E ( X ) = ∫ 0 ∞ 1 10 x e − ( x 10 ) d x Let u = x . and d v = e − ( x 10 ) d x . Then d u = 1 and v = − 10 e − ( x 10 ) Use the integration by parts to evaluate the integral, E ( X ) = ∫ 0 ∞ 1 10 x e − ( x 10 ) d x = ( 1 10 ) lim c → ∞ ( [ − 10 x e − ( x 10 ) ] 0 c </

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ISBN: 9781337825597

Author: Tan

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Chapter 10.2, Problem 22E

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Chapter 10.2, Problem 21E

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The expect time taken, to see the another plane arrive.

Solution Summary: The author describes the probability density function f defined in the interval left[a,b] associated with the continuous random variable X.

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Chapter 10 Solutions