Let X and Y be independent normal random variables with means Hx = 0, µy = 8 and standard deviation og = 3 and oy = 4. a. What are the mean and variance of X + Y? b. Simulate the distribution of X + Y and plot it. Add a normal pdf to your plot with mean and standard deviation to match the density of X +Y. (use R-code) c. What are the mean and standard deviation of 5X – Y/2? d. Simulate the distribution of 5X – Y/2 and plot it. Add a normal pdf to your plot with mean and standard deviation to match the density of 5X – Y/2. (use R-code)

Let X and Y be independent normal random variables with means Hx = 0, µy = 8 and standard deviation og = 3 and oy = 4. a. What are the mean and variance of X + Y? b. Simulate the distribution of X + Y and plot it. Add a normal pdf to your plot with mean and standard deviation to match the density of X +Y. (use R-code) c. What are the mean and standard deviation of 5X – Y/2? d. Simulate the distribution of 5X – Y/2 and plot it. Add a normal pdf to your plot with mean and standard deviation to match the density of 5X – Y/2. (use R-code)

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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Question

for simulation use R code

Ch: Estimating Random Variables
Let X and Y be independent normal random variables with means
Hx = 0, µy = 8 and standard deviation ox = 3 and oy = 4.
a. What are the mean and variance of X + Y?
b. Simulate the distribution of X + Y and plot it. Add a normal pdf to your plot
with mean and standard deviation to match the density of X + Y. (use R-code)
c. What are the mean and standard deviation of 5X – Y/2?
d. Simulate the distribution of 5X – Y/2 and plot it. Add a normal pdf to your
plot with mean and standard deviation to match the density of 5X – Y/2. (use
R-code)

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