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5. Consider the following probability density function (pdf) for some continuous random variable X defined by { * if 0saS M el sewhere = (r) (a) Find the constant M. (b) Find the variance of X denot ed V (X) (c) Find the value of 70h percentile for the continuous random variable X .

5. Consider the following probability density function (pdf) for some continuous random variable X defined by { * if 0saS M el sewhere = (r) (a) Find the constant M. (b) Find the variance of X denot ed V (X) (c) Find the value of 70h percentile for the continuous random variable X .

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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5. Consider the following probability density function (pdf) for some continuous random variable X defined by { * if 0saS M elsewhere = (r) (a) Find the const ant M. (b) Find the variance of X denoted V (X) (c) Find the value of 70*h percentile for the continuous random variable X. 6. Let X1, X2 and X3 represent the times necessary to perform three successive repair tasks at a certain facility. Suppose X1, X2 and X3 are independent normally distributed random variable with X1 ~ N (60, 15), X2 ~ N (60, 15), and X3 ~ N (60, 15). (a) Let M = X1 - X2 - Xs, then find the mean of M or , and the standard deviation of M or aM (b) Compute P(–10 <M < 5)
Transcribed Image Text:5. Consider the following probability density function (pdf) for some continuous random variable X defined by { * if 0saS M elsewhere = (r) (a) Find the const ant M. (b) Find the variance of X denoted V (X) (c) Find the value of 70*h percentile for the continuous random variable X. 6. Let X1, X2 and X3 represent the times necessary to perform three successive repair tasks at a certain facility. Suppose X1, X2 and X3 are independent normally distributed random variable with X1 ~ N (60, 15), X2 ~ N (60, 15), and X3 ~ N (60, 15). (a) Let M = X1 - X2 - Xs, then find the mean of M or , and the standard deviation of M or aM (b) Compute P(–10 <M < 5)
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