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Variable Mean(Expected Value) -8 Standard Deviation 1.5 0.3 1.1 Coefficient 3 -4 -2 a) What is the expected value of T? b) What is the variance of Y? c) What is the variance of T? d) What is the standard deviation of T? e) What is the probability that Tis within 1.5 standard deviations of its mean? f) What is the probability that T is >30? 9) What is the probability that Tis < 267 h) What is the probability that 26 14?

Variable Mean(Expected Value) -8 Standard Deviation 1.5 0.3 1.1 Coefficient 3 -4 -2 a) What is the expected value of T? b) What is the variance of Y? c) What is the variance of T? d) What is the standard deviation of T? e) What is the probability that Tis within 1.5 standard deviations of its mean? f) What is the probability that T is >30? 9) What is the probability that Tis < 267 h) What is the probability that 26 14?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Suppose X, Y, and Z are three independent normal random variables. X has an expected value of 9 and a standard deviation of 1.5; Y has an expected value of 4 and a standard deviation of 0.3; Z has an expected value of -8 and a standard deviation of 1.1. Let T = 3X + -4Y - 2Z Variable Y Mean(Expected Value) 4 -8 Standard Deviation 1.5 0.3 1.1 Coefficient -4 -2 a) What is the expected value of T? b) What is the variance of Y? c) What is the variance of T? d) What is the standard deviation of T? e) What is the probability that T is within 1.5 standard deviations of its mean? f) What is the probability that T is >30? g) What is the probability that T is < 26? h) What is the probability that 26 < T < 30? i) What is the 80th percentile of the distribution of T? j) What is the probability that the X, Y, and Z are all less than their respective 35th percentiles? k) What is the probability that X + Y > 14?
Transcribed Image Text:Suppose X, Y, and Z are three independent normal random variables. X has an expected value of 9 and a standard deviation of 1.5; Y has an expected value of 4 and a standard deviation of 0.3; Z has an expected value of -8 and a standard deviation of 1.1. Let T = 3X + -4Y - 2Z Variable Y Mean(Expected Value) 4 -8 Standard Deviation 1.5 0.3 1.1 Coefficient -4 -2 a) What is the expected value of T? b) What is the variance of Y? c) What is the variance of T? d) What is the standard deviation of T? e) What is the probability that T is within 1.5 standard deviations of its mean? f) What is the probability that T is >30? g) What is the probability that T is < 26? h) What is the probability that 26 < T < 30? i) What is the 80th percentile of the distribution of T? j) What is the probability that the X, Y, and Z are all less than their respective 35th percentiles? k) What is the probability that X + Y > 14?
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