Reference no: EM132232552
A fair coin is tossed successively three times. Let X be the number of heads on the third tossing and let Y be the total number of heads.
a) find the joint probability density function (p.d.f) of X and Y
b) Find the marginal p.d.f of X. Compute E(X) and V(X). Does X follow a classical distribution?
c)Find the marginal p.d.f of Y. Compute E(Y) and V(Y). Does Y follow a classical distribution?
d)Compute E(XY), Cov(X,Y), and p.
e)find all the conditional p.d.f 's of X given Y=y
f)Find all the conditional p.d.f's of Y given X=x
g)compute E(X|y) for the possible values y of Y
h)compute E(Y|x) for the possible values x given X
i) Are X and Y dependent or independent? Explain