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

• April 29th 2009, 11:42 AM
arslan
finding the standard deviation of the variable????
can anybody help solve this please
• April 29th 2009, 11:52 AM
Moo
Hello,
Quote:

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, $\text{Var}(X+Y)=\text{Var}(X)+\text{Var}(Y)$
• April 30th 2009, 04:54 AM
arslan
Quote:

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???
• April 30th 2009, 06:15 AM
mr fantastic
Quote:

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