Vapor asks but isnt that fraction highly variable

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 0 elsewhere. a) Graph the probability density function and the cumulative distribution function. b) What is the probability that a company chosen at random expends less than 10% of its budget on pollution controls? c) What is the probability that a company chosen at random spends more than 50% on pollution controls? d) Mr. Vapor comes to seek your advice before going into business. “What fraction of my budget can I expect to spend on pollution controls?” What do you tell him? e) Mr. Vapor asks, “But isn’t that fraction highly variable?” What can you tell him to quantify the expected variation? 3.a) F ( x) = ∫ x −∞ F ( y) = = ∫ f (t )dt , for - ∞ < x < ∞ y −∞ 1 ∫ −∞ y 6(1 − t ) 5 dt = ∫ 6(1 − t ) 5 dt =− (1 − t ) 6 0 y 6(1 − t ) 5 dt + ∫ 6(1 − t ) 5 dt =1 + 0 = 1 1 y 0 = −(1 − y ) 6 + 1 0 ≤ y ≤1 y > 1 so, Ⱥ0 Ⱥ F ( y ) = Ⱥ− (1 − y ) 6 + 1 Ⱥ 1 Ⱥ y<0 0 ≤ y ≤1 y >1 3/8 CEE 202 – Engineering Risk & Uncertainty Homework 4 Spring 2011 (Bond) Probability Distributions, Expected Values b) Find the probability of y<0.1 This value...
View Full Document

Ask a homework question - tutors are online