Mean and Variance of joint marginal pdfs?

• Nov 5th 2008, 09:17 PM
wolverine21
Mean and Variance of joint marginal pdfs?
1. Let X1, X2, X3, X4 be four mutually independent random variables, having the same pdf, f(x) = 2x, 0 < x < 1, zero elsewhere. Find the mean and variance of The sum Y, of these four random variables.

I don't even know how to start this problem. I'm trying to understand it in the book and am completely lost. All we learned how to do is turn X1 and X2 into functions of f(X1) and f(X2). Any help?
• Nov 6th 2008, 12:26 AM
mr fantastic
Quote:

Originally Posted by wolverine21
1. Let X1, X2, X3, X4 be four mutually independent random variables, having the same pdf, f(x) = 2x, 0 < x < 1, zero elsewhere. Find the mean and variance of The sum Y, of these four random variables.

I don't even know how to start this problem. I'm trying to understand it in the book and am completely lost. All we learned how to do is turn X1 and X2 into functions of f(X1) and f(X2). Any help?

$\displaystyle E(Y) = E(X_1) + E(X_2) + E(X_3) + E(X_4) = 4 E(X_1)$.

And you should know that $\displaystyle E(X_1) = \int_0^1 (x) (2x) \, dx$.

Since the $\displaystyle X_i$ are independent, $\displaystyle Var(Y) = Var(X_1) + Var(X_2) + Var(X_3) + Var(X_4) = 4 Var(X_1)$.

And you should know that:

$\displaystyle Var(X_1) = E(X_1^2) - [E(X_1)]^2$.

$\displaystyle E(X_1^2) = \int_0^1 (x^2) (2x) \, dx$.