Does y follow a classical distribution

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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

Reference no: EM132232552

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