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d) What is the standard deviation of T? e) What is the probability that T is within 2.0 standard deviations of its mean? f) What is the probability that T is >0? [

d) What is the standard deviation of T? e) What is the probability that T is within 2.0 standard deviations of its mean? f) What is the probability that T is >0? [

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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Suppose X, Y, and Z are three independent normal random variables. X has an expected value of -3 and a standard deviation of 2.5; Y has an expected value of 4 and a standard deviation of 3.1; Z has an expected value of -1 and a standard deviation of 1.1. Let T = 1X - 2Y + 3Z Variable Mean(Expected Value) Standard Deviation Coefficient 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? X f) What is the probability that T is >0? -3 2.5 1 Y e) What is the probability that T is within 2.0 standard deviations of its mean? Z 4 -1 3.1 1.1 -2 3 k) What is the probability that X + Y> 0? g) What is the probability that T is < -20? h) What is the probability that -20 < T < 0? | i) What is the 25th percentile of the distribution of T? j) What is the probability that the X, Y, and Z are all less than their respective 25th percentiles? Enter a number. 1) Copy your R script or any other comments for the above into the text box here.
Transcribed Image Text:Suppose X, Y, and Z are three independent normal random variables. X has an expected value of -3 and a standard deviation of 2.5; Y has an expected value of 4 and a standard deviation of 3.1; Z has an expected value of -1 and a standard deviation of 1.1. Let T = 1X - 2Y + 3Z Variable Mean(Expected Value) Standard Deviation Coefficient 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? X f) What is the probability that T is >0? -3 2.5 1 Y e) What is the probability that T is within 2.0 standard deviations of its mean? Z 4 -1 3.1 1.1 -2 3 k) What is the probability that X + Y> 0? g) What is the probability that T is < -20? h) What is the probability that -20 < T < 0? | i) What is the 25th percentile of the distribution of T? j) What is the probability that the X, Y, and Z are all less than their respective 25th percentiles? Enter a number. 1) Copy your R script or any other comments for the above into the text box here.
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