Suppose the random variable X~ Beta(a, 3), namely its PDF fx(x) = I(a + B) r(a)r(3)* r^-1(1−z)ß-1, 0 < x < 1, ~ Beta(a +3,7), namely its PDF I(a +8+y) fy (y) = = -yª+³−¹(1 — y)²-¹, - 0 < y < 1, r(a + 3)(y) nd X and Y are independent. Define U = XY, V = X. Find the joint PDF fuv(u, v).

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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Suppose the random variable X~ Beta(a, 3), namely its PDF
fx(x) =
I(a + 3)
r(a)(3)
-ra-1(1−z)3-1,
0 < x < 1,
Beta(a +3, y), namely its PDF
fy (y) =
I(a +8+y)
r(a + 3)(y)
¹(1 − y)*-¹, 0 < y < 1,
and X and Y are independent. Define U = XY, V = X. Find the joint PDF fuv(u, v).
Transcribed Image Text:Suppose the random variable X~ Beta(a, 3), namely its PDF fx(x) = I(a + 3) r(a)(3) -ra-1(1−z)3-1, 0 < x < 1, Beta(a +3, y), namely its PDF fy (y) = I(a +8+y) r(a + 3)(y) ¹(1 − y)*-¹, 0 < y < 1, and X and Y are independent. Define U = XY, V = X. Find the joint PDF fuv(u, v).
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