# 5) Given below is a bivariate distribution for the random variables x and y.f(x, y)xy0.250800.530500.34060Compute the covariance and correlation for x and y. Are x and y positively related, negatively related, or unrelated?Is the variance of the sum of x and y bigger, smaller, or the same as the sum of the individual variances? Why?

Question

5) Given below is a bivariate distribution for the random variables x and y.

 f(x, y) x y 0.2 50 80 0.5 30 50 0.3 40 60
1. Compute the covariance and correlation for x and y. Are x and y positively related, negatively related, or unrelated?
2. Is the variance of the sum of x and y bigger, smaller, or the same as the sum of the individual variances? Why?
Step 1

Obtain the mean of x and mean of y:

The mean of x is, sum(xf(x.y) =E(x)=37 and mean of y is, sum(yf(x.y)=E(y) =59

Step 2

Obtain the variance of x:

The variance of x is,

Step 3

Obtain the variance of y:

The varian...

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