Suppose that X and Y have the following joint probability...

Suppose that X and Y have the following joint probability distribution: f(x,y) | x | 1 | 2 | 3 ---|---|---|---|--- y | 1 | 0.05 | 0.05 | 0.1 | 2 | 0.05 | 0.1 | 0.35 | 3 | 0 | 0.2 | 0.1 a. Evaluate the marginal distribution of X; b. Evaluate the marginal distribution of Y; c. Find P(Y = 3|X = 2)

Transcript

00:01 So over the past area, to find a marginal distribution of x, which is given by the probability of x is equal to small x, which is the summation over the range of y times the probability of x is equal to x, comma, y is equal to y.

00:19 So the probability of x is equal to 1 will be equal to the probability of x is equal to 1, y is equal to 1 plus the probability of x is equal to 1 former y is equal to 2 plus probability of x is equal to 3 y will be equal to 1 so we get 0 .05 plus 0 .05 plus 0 .1 and this gives us 0 .1 and probability of x is equal to 2 will be the probability of x is equal to 2 y is equal to 1 plus probability of x is equal to 2 y is equal to 2 plus probability of x is equal to 2 y is equal to 3 so we get 0 .05 plus 0 .1 plus 0 .2 and this gives a 0 .35 the probability of x is equal to 3 will be the probability of x is equal to 3 why is equal to 1 plus probability of x is equal to 3 y is equal to 2 plus probability of x is equal to 3 y is equal to 3 and this gives us 0 .1 plus 0 .35 plus 0 .5 and this gives us 0 .55 so our marginal distribution of x is equal to x given its probability of x is equal to x given its probability of x is equal to small x will be for x.

02:06 X is equal to 1 we have 0 .10 x is equal to 2 we have 0 .35 x is equal to 3 we have 0 .55 when we come to the b -party the marginal distribution of y given x 4 of y is equal to y will be equal to the summation over the range of x times the probability of x is equal to x y is equal to y so for the probability of y is equal to one we have the probability of x is equal to one y is equal to one plus probability of x is equal to two y will be equal to one plus probability of x is equal to three y is equal to 0 .05 plus 0 .0 .0 .1.

03:06 The probability of y is equal to 2 will be equal to the probability of x to be equal to 1, y is equal to 2 plus probability of x is equal to 2, y is equal to 2 plus probability of x is equal to 3, y is equal to 2.

03:24 And this will be 0 .05, 0 .05 plus 0 .1 plus 0 .35, and this gives us 0 .50...

Question

Suppose that X and Y have the following joint probability distribution: f(x,y) | x | 1 | 2 | 3 ---|---|---|---|--- y | 1 | 0.05 | 0.05 | 0.1 | 2 | 0.05 | 0.1 | 0.35 | 3 | 0 | 0.2 | 0.1 a. Evaluate the marginal distribution of X; b. Evaluate the marginal distribution of Y; c. Find P(Y = 3|X = 2)

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