Explanation Given: is f ( x , y ) = { 1 300 e − x / 30 e − y / 10 if x ≥ 0 , y ≥ 0 0 otherwise Calculation: The objective is to find the probability to the nearest percent that the entire transaction will occur in a half hour or less. The objective is to find the probability that x + y ≤ 30 Select a random point ( x , y ) and find the probability that this point lies in the region R bounded by the coordinate axes and the line x + y ≤ 30 The probability is provided by the double integral: P [ X + Y ≤ 30 ] = ‖ R f ( x , y ) d A = ∫ 0 3030 − x 1 300 e − x 30 e − y 10 d y d x = 1 300 ∫ 0 30 e − x 30 [ e − y 10 − 1 10 ] 30 − x d x = − 1 30 ∫ 0 30 e − x 30 [ 1 − e x 10 e − 3 ] d x Simplifying further

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ISBN: 9781465208880

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 12.6, Problem 38PS

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To find: the probability to the nearest per cent that the entire transaction will occur in a half hour or less.

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Chapter 12.6, Problem 37PS

Chapter 12.6, Problem 39PS

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the probability to the nearest per cent that the entire transaction will occur in a half hour or less.

Solution Summary: The author explains how to find the probability to the nearest percent that the entire transaction will occur in a half hour or less.

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To find: the probability to the nearest per cent that the entire transaction will occur in a half hour or less.

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Chapter 12 Solutions