State whether the following are True or False with explanation:

1. Let (X,Y) be jointly distributed random variables with joint pmf p(x,y) , where p(x,y)=g(x)+h(y) for some functions g and h. Then X and Y are independent.
2. If X is a random variable, then E[X2]E[X]
3. For events A and B, if P(AB)=P(A), then A and B are independent
4. Let X1, X2,.... be a sequence of i.i.d random variables with mean . Then limnE[maxX1,X2,...,Xn]=. That is, the expected value of the largest value among X1,X2,....,Xn will approach .
5. Let Y be a Geometric random variable. Then the conditional distribution of (Y1) given Y2 is equal to the distribution of Y.
6. Let X and Y be jointly distributed random variables with finite variances, that satisfy Var(XY)=0. Then Cov(X,Y)=0.