SOLUTION: Suppose that X and Y Have the following joint probability distribution
f(x,y) x 2 4
1 0.10 0.15
y 3 0.20 0.30
5 0.10 0.15
a. Find the marginal distribution of X.
b. Fin
Question 1205407: Suppose that X and Y Have the following joint probability distribution
f(x,y) x 2 4
1 0.10 0.15
y 3 0.20 0.30
5 0.10 0.15
a. Find the marginal distribution of X.
b. Find the marginal distribution of Y.
Found 2 solutions by moonwhisperer, Edwin McCravy:Answer by moonwhisperer(1) (Show Source): You can put this solution on YOUR website! Soln : marginal of x has two values for x=2 and x=4
For x = 2, we need to find sum of all y values over x=2
i.e. (2,1)+(2,3)+(2,5) = 0.1 + 0.2 + 0.1 = 0.4
For For x = 4, we need to find sum of all y values over x=4
i.e. (4,1)+(4,3)+(4,5) = 0.15 + 0.3 + 0.15 = 0.6
To check marginal pdf of x sum to 1 = 0.4+ 0.6
Similarly,
marginal of y has three values for y=1, y=3 and y=5
For y=1, we need to find sum of all x values over y=1
i.e. (2,1)+(4,1) = 0.1 + 0.15 = 0.25
For y=3, we need to find sum of all x values over y=3
i.e. (2,3)+(4,3) = 0.2 + 0.3 = 0.5
For y=5, we need to find sum of all x values over y=5
i.e. (2,5)+(4,5) = 0.1 + 0.15 = 0.25
To check marginal pdf of y sum to 1 = 0.25+ 0.5 + 0.25