You are given the following joint pdf for the random variables X and Y :
(a) Find the marginal pdf of X.
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You are given the joint pdf of the random variables, X and Y
(a) What is the marginal distribution of X.
(b) What is the marginal distribution of Y
(c) Find the conditional distribution of X.
(d) Find E(X), where this is defined, what restrictions, if any, do we impose?
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
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?
Let X and Y be continuous random variables with joint density function.
(a) Find the marginal densities of X and Y.
(b). Are X and Y independent?
(c). Find P (X< 1/2, Y <1)
