You are given a fair die, i.e. the outcomes of any throw are contained in the sample space Let the event A be that an even number is thrown and the event B that a multiple of three is thrown. Now consider the two random variables X and Y. X takes on a value of 1 if the event A has occurred and the value 0 if A has not occurred. The random variable Y takes on the value of 1 if the event B has occurred and the value zero if B has not occurred.
(a) Derive the joint pdf of X and Y. Provide this in the form of a table
Y=0 Y=1
X=0
X=1
b) What is the marginal probability distribution of Y? (c) What is the conditional probability distribution of X, given that Y = 1? (d) What is E (X|Y = 1)? (e) What is Cov (X, Y )? (f) Are X and Y independent random variables?
