Make a simulation to verify the following theorem: if X1 ∼ N(µ1, (σ 1)^2 ), X2...

Make a simulation to verify the following theorem: if X1 ∼ N(µ1, (σ 1)^2 ), X2 ∼ N(µ2, (σ2)^ 2 ), and X1 and X2 are independent, then X1 + X2 ∼ N(µ1 + µ2, (σ2)^2+ (σ 2 )^2 ).

Solutions

Expert Solution

Above simulation Done in R. You can use any tool to do the same.

R code below for copying and run in R.

#Code Start

x1=rnorm(n=10000,mean = 10,sd = 3)
x2=rnorm(n=10000,mean = 20,sd = 4)
ans=x1+x2
#Now for the result we want the mean to be mu1+mu2=10+20=30
#And stdvariance = sd1^2+sd2^2 = 3^2+4^2 = 25
#Let's verify
mean1=mean(ans)
var1=var(ans)
mean1
var1

#Code end

Hope the above answer has helped you in understanding the problem. Please upvote the ans if it has really helped you. Good Luck!!

milcah answered 9 months ago

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