Let the joint probability density function of two discrete random X and Y be given as:
i) Find the marginal distribution of X and Y.
ii) Find the conditional distribution of X given Y=1.
iii) Test the independence of variable s X and Y.
iv) Find V
Let ( ,X Y) have the joint p.d.f. given by:
f(x,y)=
i) Find the marginal p.d.f.’s of X and Y.
ii) Test the independence of X and Y.
iii) Find the conditional distribution of X given Y = .y
iv) Compute (E X | Y = )y and (E Y | X = ).x
State whether the following statements are True or False. Justify your answer with a short proof or a counter example:
a) If P is a transition matrix of a Markov Chain, then all the rows of lim Pnare identical.
b) In a variance-covariance matrix all elements are always positive.
c) If X1, X2 ,X3 , are iid from N2 ( µ , ), then
d) The partial correlation coefficients and multiple correlation coefficients lie between −1 and 1.
e) For a renewal function
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