Solve the below:
1) Two socks are randomly drawn, without replacement, from a drawer containing 2 green sock, 3 black socks, and 4 red socks. Let X be the number of green socks and let Y be the number of black socks among the two socks that have been drawn.
a) Draw a two- way distribution table representing the joint distribution of X and Y
b) Find a formula for the joint p.d.f f(x,y) of X and Y
c) Find the marginal distribution table of X and Y
d) Compute µx, µy, V(x), and V(y)
e) Compute E(X,Y) and the covariane between X an Y
f) Compute the value of the coefficient of linear correlation p
g) Find the conditional distribution table of Y, given X=1
h) Compute E(Y|1) and V(Y|1)
i) Are X and Y independent? Explain you answers.
2) Let the joint p.d.f. of X and Y be given by f(x,y) = c (x^2 + Y^2, for x=-1, 0,1,3 and y = -1,2,3 where c is a constant.
a) Find the value of c
b) Find the conditional distribution table of X, given that Y=2
c) Compute P(X>2-Y)
d) Compute Cov(X,Y)