Answer the following using R code.Answer the following using R code. Suppose Z i

Question

Answer the following using R code.Answer the following using R code. Suppose Z is a standard normal random variable. Suppose X is a normal random variable with mean 4 and standard deviation 5. Answer the following using R code.

c) What is the expected value of the random variable 5X - 3 using R code?

d) What is the standard deviation of the random variable (x-4) / 5 using R code?

e) If X and Z are independent then what is the variance of 2X - 4Z using R code?

d) What is the standard deviation of the random variable 5X - 3?

Explanation / Answer

# Z is saatandard normal distribution (0,1), E(z)=mu=0, sd(z)=1 that is Var(z)=1
# X is normal distribution (mu=4 , sd=5), E(x)=mu=4, sd(x)=5 that is Var(x)= 25.
mean_z=0
sd_z=1
var_z=1
mean_x=4
sd_x=5
var_x=25

# C) E(5x-3)=5*E(x)-3 = 5*mean_x-3
5*mean_x-3

#d) sd_((x-4)/5)= sd_x/5 # Because standard deviation of constant is zero
sd_x/5

#e) var(2x-4z)= 4*var(x)-16*var(z)= 4*var_x-16*var_z
4*var_x-16*var_z

#f)sd(5x-3)=5*sd_x # Because standard deviation of constant is zero
5*sd_x

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