Need Help.. Suppose Z is a standard normal random variable. Suppose X is a norma

Question

Need Help..

Suppose Z is a standard normal random variable. Suppose X is a normal random variable with mean 7 and standard deviation 2. Answer the following using R code.

a) Calculate the 37th percentile of the distribution of Z.

b) Calculate the 37th percentile of the distribution of X.

c) What is the expected value of the random variable X - 7?

d) What is the variance of the random variable X - 7?

e) What is the variance of the random variable X - 7/2 ?

f) If X and Z are independent then what is the variance of Z - X?

g) Copy your R script for the above into the text box here.

Explanation / Answer

i will answer 1st 4 subparts only

using R

a)

Normal with mean = 0 and standard deviation = 1

-0.331853

b)

Normal with mean = 7 and standard deviation = 2

6.33629

c) to find E(X-7)=7-7=0( since X~N(7,2) distribution )

d) to find

Var(X-7)=var(X)=4

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