- #1
rooski
- 61
- 0
Homework Statement
Discrete random variables X and Y , whose values are positive integers, have the joint probability mass function , (, ) = 2−−. Determine the marginal probability mass functions () and (). Are X and Y independent? Determine [], [ ], and [ ].
The Attempt at a Solution
y=1ʃ∞ pX(x) = Σ pX,Y(x,y)
= y=1ʃ∞ Σ 2^(-x-y)
= y=1ʃ∞ 2^(-x) Σ 2^(-y)
= 2^-x
x=1ʃ∞ pY(y) = Σ pX,Y(x,y)
= x=1ʃ∞ Σ 2^(-x-y)
= x=1ʃ∞ 2^(-y) Σ 2^(-x)
= 2^-y
Since pX,Y(x, y) = pX(x) * pY(y), X and Y are independent of each other.
I am stuck figuring out the expectations. Are we to assume that x and y can only take the values 0 and 1? The expectation requires a weighted average of all the possible values of x and y but the problem does not tell us the possible values...