The next three questions use the following joint probability table. Fill in the missing values.
S = 10 S = 20 S = 30 P(A=a)
A = 5 G .625
A = 10 .1 .125
P(S=s) .25 .15 1
a. What is the value of G?
b. What is the value of E[A|S=10]?
c. Is the covariance of A and S positive, negative, or zero. I'm not asking for a number. Any way you can figure this out is fine, but provide a justification.