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Thread: Variance of Y question

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    Variance of Y question




    Hi all,

    I'm struggling on a variance of Y question that goes like this:

    Let X follow an exponential distribution with a mean of theta. Let Y = X^2. What is the variance of Y?

    From what I've gathered, we need to use the definition V(Y) = E(Y^2)-E(Y)^2 and also use integration (by parts??)...

    Any help or suggestions would be greatly appreciated.

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    Re: Variance of Y question

    You can find the distribution of X^2 and from that find the variance.
    F_Y(y)=P(Y\leq y)=P(X^2\leq y)=P(X\leq \sqrt{y})
    f_Y(y)=\frac{dF_Y(y)}{dy}
    Var(Y)=E[Y^2]-E[Y]^2
    The difference between stupidity and genius is that genius has its limits.
    "Albert Einstein"

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    Re: Variance of Y question


    Thank you for the response!!

    So if the distribution for expo is: lambda*e^(-lambda*x)
    Does that mean we add X^2 instead of X? Where does integration come in?

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