Show that the random vatiables with the densities f(l:, y) = X + Y and g(x, y) = (x +

Chapter 24, Problem 24.1.154

(choose chapter or problem)

Show that the random vatiables with the densities

f(x, y) = X + Y

and

\(g(x, y)=\left(x+\frac{1}{2}\right)\left(y+\frac{1}{2}\right)\)

If \(0 \leqq x \leqq 1,0 \leqq y \leqq 1\) and and f(x. y) = 0 and g(x. y) = 0 elsewhere. have the same marginal distribution.

Text Transcription:

g(x, y) = (x + 1/2) (y + 1/2)

0 <= x <= 1, 0 <= y <= 1

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