(Step-by-Step) X and Y are i.i.d. random variables with common p.d.f. f_X(x)=e^-xu(x), f_Y(y)=e^-yu(y) Find the p.d.f. of the following random variables X+Y,
Question: X and Y are i.i.d. random variables with common p.d.f.
\[{{f}_{X}}\left( x \right)={{e}^{-x}}u\left( x \right),\,\,\,\,{{f}_{Y}}\left( y \right)={{e}^{-y}}u\left( y \right)\]Find the p.d.f. of the following random variables
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X+Y, (b) X - Y, (c) XY, (d) X /Y.
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Solution: Prove that adding 12 i.i.d. RVs each on U(0,1) yields
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[Solution Library] Take two Gaussian RVs X and Y generated from part
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(See Solution) The joint p.d.f. of the random variables X and
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(Step-by-Step) Suppose the density function of X is an even function.
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[See Solution] Suppose X and Y are independent normal random variables.
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![[Solution Library] Take two Gaussian RVs X](/images/solutions/MC-solution-library-72193.jpg "[Solution Library] Take two Gaussian RVs X and Y generated from part")
![[See Solution] Suppose X and Y are](/images/solutions/MC-solution-library-72196.jpg "[See Solution] Suppose X and Y are independent normal random variables.")
