A joint PMF pX Yxi yj has the values shown in the table belo

A joint PMF p_X, Y[x_i, y_j] has the values shown in the table below: Which of the following values represents the conditional PMF P[Y=2 | X=l] (equivalently p_Y|X[2|1])? 0.1 0.2 0.3 0.4

Solution

The joint probability mass function of two discrete random variables XX and YYis defined as

PXY(x,y)=P(X=x,Y=y).

PXY(x,y)=P(X=x,Y=y)=P((X=x) and (Y=y)).

(xi,yj)RXYPXY(xi,yj)=1(xi,yj)RXYPXY(xi,yj)=1

Conditional probability mass function (pmf) pX|Y (x | y) = P{X = x | Y = y} = P{X = x, Y = y} P{Y = y} = p(x, y) pY (y) defined for y : pY (y) > 0.

so the answer is b