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Math Help - Finding a density function.

  1. #1
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    Finding a density function.

    A friend of mine was asking me for help with this exercise, and I'm not sure how to tackle it, could someone please help me.

    a) We are given a density function for the random variables Y_1 and Y_2
    f(y_1 , y_2)=\begin{cases} e^{-y_1} &\quad\text{ if }\quad 0\leq y_2 \leq y_2 \leq \infty \\ 0  &\text{elsewhere}\end{cases}

    Now we are given a new random variable U=Y_1 - Y_2, and we need to find the density function for U.

    b) Find \mathbb{E}[U] and \mathbb{V}[U]

    I could appreciate some help, I have not yet studied integrals in multiple variables, but I'm not sure if I have to do that for this problem.
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  2. #2
    MHF Contributor matheagle's Avatar
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    You can either obtain the CDF or transform to U and W, where W is any other variable you wish.
    However, all of this assumes you've seen multivariate calculus.
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