1. For the experiment of throwing a normal six-faced die, let X 1,2,...,6 represent the number of dots that results. a. What is the expected value or E(X) = ? b. What is the variance of X, or Var (X) =? Note that Var (X)= E(X-E(X)) 2. Suppose you throw a die and a coin at the same time. Let X =-1 if tails and X = +1 if heads. Meanwhile let Y = 1, 2,... 6 represent the number that shows on the face of the die. a. Fill up the following table with the joint probabilities, which is also the joint probability density function for X and Y. Heads or X=1 Tails or X=-1 Y=1Y 2Y 3Y-4Y-5Y-6 b. Suppose you are told that the coin turns up as heads. Fill up the following table representing the conditional probability density function of Y, conditional that a head has turned up; i.e. X = 1. Probability Y=1Y 2Y=3Y=4Y=5Y=6 c. What is E(Y|X=1)?