Question
Asked Dec 6, 2019
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7.4. If X and Y have joint density function
( 1/y, if0 < y < 1, 0 < x < y
o,
fx,Y (x, y)
otherwise
find
a. E[XY]
b. E[X]
c. E[Y]
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7.4. If X and Y have joint density function ( 1/y, if0 < y < 1, 0 < x < y o, fx,Y (x, y) otherwise find a. E[XY] b. E[X] c. E[Y]

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Step 1

Given Joint Density function

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if 0 < y < 1,0 < x < y! fxy (x, y) = 0, otherwise a) E(XY) is given by - ||shotanar-||orjar-||-i{r»-| Sordy= E(XY) = || xyfxx (x, y)dxdy =: хух —dxdy dy

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Step 2

b) E(X) is given by

Computing Marginal density of x

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f-(x) = | fxx(x, y)dy | fxx (x, y)dy dy = [In ylb = x(In 1 – In 0) Natural Log is not defined at 0 So, E(X) Does not exist

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Step 3

c)E(Y) is given by

Computing Ma...

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y -(y – 0) = 1 -dx fxx(x, y)dx : y fy(y) = r0m- įmou-įso-| E(Y) = | yfrV)dx = | ydy 2

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