# Normal RV

#### dlee

##### New member
If X ~ N(2,4) then Y = -X-1 is also a normal random variable such that Y ~ N(μ,σ^2).
Find μ and σ^2.

I know that E(X) = 2 and Var(X) = 4.

E(Y) = -E(X) - 1
E(Y) = -2 - 1 = -3
So I found μ, but I'm not sure how to find the variance. Help?

#### Klaas van Aarsen

##### MHB Seeker
Staff member
If X ~ N(2,4) then Y = -X-1 is also a normal random variable such that Y ~ N(μ,σ^2).
Find μ and σ^2.

I know that E(X) = 2 and Var(X) = 4.

E(Y) = -E(X) - 1
E(Y) = -2 - 1 = -3
So I found μ, but I'm not sure how to find the variance. Help?
Welcome to MHB, dlee!

There are a couple of basic properties for expectations and variances as you can see here.

In particular $\sigma^2(X + a)=\sigma^2(X)$ and $\sigma^2(aX)=a^2\sigma^2(X)$, where $a$ is some arbitrary constant.

#### dlee

##### New member
AH the variance is 4! Thank you!