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.
|
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RB
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0.40
|
0.00
|
|
RA
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0.40
|
½ - ∈
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∈
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0.00
|
∈
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½ - ∈
|
1. Find the mean and variance of RA. What about RB?
2. Find the covariance and correlation coefficient between RA and RB.
Let RP = ½ RA + ½ RB represent the return on a 50/50 mix of the two assets.
1. If ∈ = 0, what is the distribution of RP?
2. If ∈ = 0.10, what is the distribution of RP? Compare the answer with the previous question. What are E(RP) and V ar(RP)?
3. Is RP preferable to RA or RB?
4. For any ∈ which is slightly bigger than zero, do you still have the same conclusion as in the last part?