Given below is a bivariate distribution for the random variables x and y.
f(x,y) | x | y |
0.1 | 90 | 70 |
0.5 | 20 | 30 |
0.3 | 40 | 60 |
a. Compute the expected value and the variance for x and y.
b. Develop a probability distribution for x + y.
c. Using the result of part (b), compute E(x+y) and Var (x+y).
d. Compute the covariance and correlation for x and y. Are x and y positively related, negatively related or unrelated?
e. Is the variance of the sum of x and y bigger, smaller, or the same as the sum of the individual variances? Why?
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Given below is a bivariate distribution for the random variables x and y. f(x,y) x y...
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Suppose that X and Y form a bivariate normal distribution. You are given that E[X] = E[Y] = 0, with o x = 3, 0y = 2. Further, the correlation between X and Y is 0.5. Find P(X<Y + 1).
Suppose that X and Y form a bivariate normal distribution. You are given that E[X] = E[Y] = 0, with o x = 3, 0y = 2. Further, the correlation between X and Y is 0.5. Find P(X<Y + 1).