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Math Help - Mean and Variance of joint marginal pdfs?

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    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?
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    Quote Originally Posted by wolverine21 View Post
    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?
    E(Y) = E(X_1) + E(X_2) + E(X_3) + E(X_4) = 4 E(X_1).

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


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

    And you should know that:

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

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