1. If

*X1*~

*N*(μ, σ2) and

*X*2 ~

*N*(μ, σ2) are normal random variables, then what is the difference between 2

*X*1 and

*X*1 +

*X*2? Discuss both their distributions and parameters.

I try the following solution however I am unable to identify any differences. Please help.

Assume that

*X*1 +

*X*2 have same μ =1, σ = 2

2

*X*1 = 2(1,22) = 2(1,4) = (2,8)

*X*1 +

*X*2 = (1 + 1, 22 + 22) = (2,8)