# Math Help - finding the standard deviation of the variable????

1. ## finding the standard deviation of the variable????

can anybody help solve this please

2. Hello,
Originally Posted by arslan
can anybody help solve this please
For any rv X and Y, $\mathbb{E}(X+Y)=\mathbb{E}(X)+\mathbb{E}(Y)$

For any independent rv X and Y, $\text{Var}(X+Y)=\text{Var}(X)+\text{Var}(Y)$

3. Originally Posted by Moo
Hello,

For any rv X and Y, $\mathbb{E}(X+Y)=\mathbb{E}(X)+\mathbb{E}(Y)$

For any independent rv X and Y, $\text{Var}(X+Y)=\text{Var}(X)+\text{Var}(Y)$
how???

4. Originally Posted by arslan
how???
E(X + Y) = E(X) + E(Y) is easily proved from the definition of expected value.

For the proof of Var(X + Y) = Var(X) + Var(Y), read this: Variance of the Sum of Two Independent Random Variables