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Unformatted text preview: . 2 (b) (4%) Find the density of the random variable Z = X + Y .
Sol) From theorem for the sums of gamma distributed random variables, we immediately have
Z ∼ Γ(9/2, 2). Therefore,
fZ (z ) = 29/2 7/2 −2z
Γ(9/2) z>0 5. (4%) Let X and Y be jointly continuous with joint probability density function given by 1
for 1 < x < ∞ and 1 < y < ∞
x2 y 2
f (x, y ) =
Find the probability density function of U = XY .
Sol) It is clear that I (U ) = (1, ∞). Consider u ∈ I (U ). We have
∞ fU (u) =
, 1 < u < ∞.
u2 6. Suppose that the time interval between arrivals of busses to a particular stop is a random variable X (in hours)
with exponential distribution and parameter λ = 2 (arrivals/hour).
(a) (4%) You arrive, panting, to t...
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- Fall '09