The table of joint probability mass function of a pair of ra

The table of joint probability mass function of a pair of random variables (X, Y), is given by Write down the probability mass function of X. Find the mean of X. Find P(X 0).

Solution

PX(0) = PXY(0,0)+ PXY(0,1) + PXY(0,2) = 1/9 + 2/9 + 1/9 = 4/9...
PX(1) = 2/9 + 2/9 + 0 = 4/9....
PX(2) = 1/9 + 0+0 = 1/9....

PX(x) = 4/9 when x=0.........
   = 4/9 when x=1.........

= 1/9 when x=2.......

b)mean of x = 0*(4/9) + 1*(4/9) + 2*(1/9) = 6/9 = 2/3....

c) P [ X <=1 , Y > 0 ] = PXY[0,1]+ PXY [0,2] + PXY[1,1] + PXY[1,2] = 2/9 + 1/9 + 2/9 + 0 = 5/9..