Consider the random variables:

X= the first year rate of return(%) expected from project A, and

Y= the first year rate of return(%) expected from project B.

The table below gives the joint probability function P(x,y):

X

-10 0 20 30

10 0.15 0.06 0.09 0.11

Y 20 0.09 0.03 0.28 0.19

Answer the following questions, rounding your answers to two decimal places where appropriate

(a)Find the marginal probability function of Y . In particular, find

i.PY(10)=P(Y=10)=?

ii.PY(20)=P(Y=20)=?

(b)Find the probability that the return from project B is 20 percent given that the return from project A is 20 percent.

(c)What is the expected rate of return from project A,E(X)?

(d)What is the expected rate of return from project B, E(Y)?

(e)What is the covariance betweenXandY?