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?
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
- Given the below is a bivariate distribution for the random variables x and y.
|
Economic Scenario |
|
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 andcorrelation for x and y. Are x and y positively related, negatively related, or unrelated?
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