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.

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:

      X       0                  1

Y                                              

1           0.9200        0.3080

2          0.0506        0.1694

3          0.0874         0.2926

2,160 π

step-by-step explanation:

3

step-by-step explanation:

because where the point where the 2 lines intersect is (3,-1) the x value is 3