11. The marginal density functions for independent random variables X and Y are g(x) and h(y). Find the joint probability density function f(x, y) for the independent random variables X and Y. Your answer should be a piecewise function. = { x + / / / 2 0 g(x): 0 < x < 1 elsewhere h(y) = + 0 0 < y < 1 elsewhere

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11. The marginal density functions for independent random variables X and Y are g(x) and
h(y). Find the joint probability density function f(x, y) for the independent random
variables X and Y. Your answer should be a piecewise function.
= { x + /
2
0
g(x):
0 < x < 1
elsewhere
h(y)
=
+
0
0 < y < 1
elsewhere
Transcribed Image Text:11. The marginal density functions for independent random variables X and Y are g(x) and h(y). Find the joint probability density function f(x, y) for the independent random variables X and Y. Your answer should be a piecewise function. = { x + / 2 0 g(x): 0 < x < 1 elsewhere h(y) = + 0 0 < y < 1 elsewhere
8. The density function for the random variable X is f(x). Find E(3X - 1).
) = √(= (2x + 1
(2x + 1)
E(3X - 1) =
f(x) =
1 < x < 2
0 elsewhere
Transcribed Image Text:8. The density function for the random variable X is f(x). Find E(3X - 1). ) = √(= (2x + 1 (2x + 1) E(3X - 1) = f(x) = 1 < x < 2 0 elsewhere
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