The random variable X can take on the values 3, 4, and 5, and the random variable Y can take on the values

1, 2, and 3. The joint probability distribution of X and Y is given in the following table:

Y

3 4 5

X

1 0.10 0.10 0.10

2 0.10 0.20 0.10

3 0.10 0.05 0.15

2.A. Describe in words and notation the event that has probability 0.15 in the table. .

2.b. _______________Calculate the marginal distribution of X.

2.C Calculate the population mean of X.

2.d. _______________ Calculate the population variance of X.

2.e. _______________ Graph the probability distribution and show the mean in the graph.