Question

The distributions of X and of Y are described here. If X and Y are independent, determine the joint probability distribution of X and Y.

Answer 1

Answer:

The joint probability distribution of X and Y is shown below.

Step-by-step explanation:

The distributions of X and of Y are described as follows:

    X :    0           1

P (X) : 0.23      0.77

     Y :    1            2          3

P (Y) : 0.40     0.22     0.38

It is provided that X and Y are independent.

That is:

P (X ∩ Y) = P (X) × P (Y)

Compute the joint probability distribution of X and Y as follows:

$P(X=0,Y=1)=P(X=0)\times P(Y=1)=0.23\times 0.40=0.92\\\\P(X=0,Y=2)=P(X=0)\times P(Y=2)=0.23\times 0.22=0.0506\\\\P(X=0,Y=3)=P(X=0)\times P(Y=3)=0.23\times 0.38=0.0874\\\\P(X=1,Y=1)=P(X=1)\times P(Y=1)=0.77\times 0.40=0.308\\\\P(X=1,Y=2)=P(X=1)\times P(Y=2)=0.77\times 0.22=0.1694\\\\P(X=1,Y=3)=P(X=1)\times P(Y=3)=0.77\times 0.38=0.2926$

      X       0                  1

Y                                              

1           0.9200        0.3080

2          0.0506        0.1694

3          0.0874         0.2926