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    Intuitive reason absolute values are used for transformations in statistics?

    Homework Statement Homework Equations The Attempt at a Solution this isn't really homework, but I was just wondering if someone could offer an intuitive reason as to why when random variables are transformed, we use absolute values of derivative of those functions, as opposed...
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    Expected value and variance of a conditional pdf (I think I have it)

    Homework Statement Suppose the distribution of X2 conditional on X1=x1 is N(x1,x12), and that the marginal distribution of X1 is U(0,1). Find the mean and variance of X2. Homework Equations Theorem: E(X_{2})=E_{1}(E_{2|1}(X_{2}|X_{1}))...
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    Finding a marginal pmf

    Homework Statement Suppose that X1 and X2 have the joint pmf f(x_{1},x_{2})=p^{2}q^{x_{2}},x_{1}=0,1,2,...,x_{2},x_{2}=0,1,2,... with 0<p<1,q=1-p Homework Equations The Attempt at a Solution I'm confused because the expression doesn't have x_1 in it. So usually, if I want to...
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    Statistics proof regarding integration of cdf

    Homework Statement For any cdf F(x) of a continuous random variable, show that \int_{-\infty}^{\infty}[F(x+b)-F(x+a)]dx=b-a for any a<b. Homework Equations The Attempt at a Solution Not really sure where to begin. I figure I can split the integrals and do u subs, and (after...