1) Consider two random variables with the following joint density function: 1 f(x,y) = · ab 0

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A1
1) Consider two random variables with the following joint density function:
f(x,y) =
1
0 <x <a and 0<y<b
ab
if a < b, find:
a) P{X+Y<}
b) {Ys 20)
За)
2) Two random variables X and Y have a joint probability density function:
5
x²y,
fxy (x, y) = {16
0,
elsewhere
a) Find the marginal density functions of X andY.
b) Are X and Y statistically independent?
Transcribed Image Text:1) Consider two random variables with the following joint density function: f(x,y) = 1 0 <x <a and 0<y<b ab if a < b, find: a) P{X+Y<} b) {Ys 20) За) 2) Two random variables X and Y have a joint probability density function: 5 x²y, fxy (x, y) = {16 0, elsewhere a) Find the marginal density functions of X andY. b) Are X and Y statistically independent?
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