Solve (F,G,H,i) only Please!!! 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 + 3ZVariableMean(Expected Value)Standard DeviationCoefficienta) 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?Xf) What is the probability that T is >0?-32.51Ye) What is the probability that T is within 2.0 standard deviations of its mean?Z4-13.1 1.1-23k) 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.

As per bartleby guidelines we can solve only first three subparts and rest can be reposted

Answered: f) What is the probability that T is…

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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f) What is the probability that T is >0? 9) What is the probability that T is < -20? [ h) What is the probability that -20 < T <0? [