Compute the Var$(X_1+X_2+X_3)$ and other Variances.

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The problem said;

Let $ X_1, X_2, X_3 $ be independent and identically distributed random variables each with mean $0$ and variance $1$. Below I state the work I did so far, I need help specifically in point b. If someone know how. It will be appreciated. Thanks!

a) Find Var$(3X_1) $.

Then Var$(3X_1)=\;9\text{Var}$$(X_1)=9\cdot1=9$

(b) Find Var$(X_1 + X_2 + X_3)$.

Var$(X_1)+$Var$(X_2)+$Var$(X_3)=3$

(c) Find Cov$(X_1 + X_2,X_2 + X_3)$.

Cov$(X_1+X_2, X_2+X_3) = \;$Cov$(X_1, X_2+X_3) + $Cov$(X_2,X_2+X_3)= \;$Cov$(X_2, X_2+X_3)=\;$Cov$(X_2,X_2)+$Cov$(X_2,X_3)=\;$Cov$(X_2,X_2)=\;$Var$(X_2)=1$

Looks simple and I'm worried if I miss some key step. Thanks.