Given the below is a bivariate distribution for the random variables x and y. Economic Scenario Probability of Occurrence Stock Fund (x) Bond Fund (y) Recession 0.10 -40 30 Weak Growth 0.25 5 5 Stable Growth 0.50 15 4 Strong Growth 0.15 30 2   Compute the expected value and the variance of x and y. Develop a probability distribution for x+y. Using the results of part (b), compute E(x+y) and Var(x+y). Compute the covariance and correlation for x and y. Are x and y positively related, negatively related, or unrelated?

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter9: Sequences, Probability And Counting Theory
Section9.7: Probability
Problem 1SE: What term is used to express the likelihood of an event occurring? Are there restrictions on its...
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  1. Given the below is a bivariate distribution for the random variables x and y.

Economic Scenario

Probability of Occurrence

Stock Fund (x)

Bond Fund (y)

Recession

0.10

-40

30

Weak Growth

0.25

5

5

Stable Growth

0.50

15

4

Strong Growth

0.15

30

2

 

  1. Compute the expected value and the variance of x and y.
  2. Develop a probability distribution for x+y.
  3. Using the results of part (b), compute E(x+y) and Var(x+y).
  4. Compute the covariance and correlation for x and y. Are x and y positively related, negatively related, or unrelated?
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