You MUST write a brief explanation to justify your answer. No explanation=no credit. Partially correct explanation=partial credit.??
a. For the events A and B, if (A∩B)' =S (where S, of course, is the sample space), then the events CANNOT be mutually exclusive.??
b. In a confidence interval for the difference between n matched pairs of observations, the t-distribution to use is with 2n-2 degrees of freedom.???
c. All else equal, in a hypothesis test, if we increase n, we increase α. ???
d. In a linear regression, all else equal, if SST increases, r² decreases.


2.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.? 


3.Suppose there are three events, A, B and C. B and C are mutually exclusive. P(A∩C)=.6. P(A∩B)=.25. P(C)=.5. What is P(A∩B|C)? (Or put another way, conditional on C, what is the probability of both A and B?)