Two-face has batman in a corner now its time to flip his

Question

Econ 310, Spring 2014- Week 4:

Problem 1- Finally, Two-face has Batman in a corner. Now it's time to flip his coin to decide the fate of Batman. To add fun to the gamble, Two-face decides to flip his coin three times. (Suppose his coin his fair.)

1. Define a sample space S and probability measure P representing possible outcomes of the coin flips.

2. Let X denote the number of heads. Define the random variable X as a function from S to {0, 1, 2, 3}.

3. Determine the distribution of X.

4. Compute the expected value, variance, and standard deviation of X.

5. Two-face tells Batman that at least two heads will cost him his life. Batman couter-proposes to make it three. How much will Batman's chances of survival improve if Two-face accepts the proposal?

Problem 2- The table below contains the joint distribution of the random variables RA and RB representing the percentage returns on Acme Inc, and Biloxi Co.

		RB
		0.40	0.00
RA	0.40	½ - ∈	∈
	0.00	∈	½ - ∈

1. Find the mean and variance of R_A. What about R_B?

2. Find the covariance and correlation coefficient between R_A and R_B.

Let RP = ½ R_A + ½ R_B represent the return on a 50/50 mix of the two assets.

1. If ∈ = 0, what is the distribution of R_P?

2. If ∈ = 0.10, what is the distribution of R_P? Compare the answer with the previous question. What are E(R_P) and V ar(R_P)?

3. Is R_P preferable to R_A or R_B?

4. For any ∈ which is slightly bigger than zero, do you still have the same conclusion as in the last part?