Question

2. There are two stocks (stock 1 and stock 2) whose returns are random and denoted by X and Y. The joint probability distribution of X and Y are given by: x 0% 4% y 1% .25 .25 3% .25 .25 a. Find Cov(X, Y) and Corr(X, Y). Are X and Y statistically independent? b. Suppose that you invest 50% of your wealth in stock 1 and 50% of your wealth in stock 2. Let R denote return on your investment portfolio. i. What is the probability that R will be less than or equal to 1%? ii. Calculate E(R) and Var(R).

          2. There are two stocks (stock 1 and stock 2) whose returns are random and denoted by X and Y. The joint probability distribution of X and Y are given by:

        x
        0%      4%
y   1%  .25     .25
    3%  .25     .25

a. Find Cov(X, Y) and Corr(X, Y). Are X and Y statistically independent?
b. Suppose that you invest 50% of your wealth in stock 1 and 50% of your wealth in stock 2. Let R denote return on your investment portfolio.
    i. What is the probability that R will be less than or equal to 1%?
    ii. Calculate E(R) and Var(R).

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2. There are two stocks (stock 1 and stock 2) whose returns are random and denoted by X and Y. The joint probability distribution of X and Y are given by:

x
0% 4%
y 1% .25 .25
3% .25 .25

a. Find Cov(X, Y) and Corr(X, Y). Are X and Y statistically independent?
b. Suppose that you invest 50% of your wealth in stock 1 and 50% of your wealth in stock 2. Let R denote return on your investment portfolio.
i. What is the probability that R will be less than or equal to 1%?
ii. Calculate E(R) and Var(R).

Added by Andrea M.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Adi S

09/16/2023

Step 1

Cov(X, Y) is given by the formula: Cov(X, Y) = E(XY) - E(X)E(Y) To find E(XY), we need to multiply the returns of each stock by their joint probabilities and sum them up: E(XY) = (0% * 25) + (4% * 25) + (1% * 3%) E(XY) = 0 + 1 + 0.03 = 1.03 Now, we need to Show more…

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2. There are two stocks (stock 1 and stock 2) whose returns are random and denoted by X and Y. The joint probability distribution of X and Y are given by: x 0% 4% y 1% .25 .25 3% .25 .25 a. Find Cov(X, Y) and Corr(X, Y). Are X and Y statistically independent? b. Suppose that you invest 50% of your wealth in stock 1 and 50% of your wealth in stock 2. Let R denote return on your investment portfolio. i. What is the probability that R will be less than or equal to 1%? ii. Calculate E(R) and Var(R).

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