Question

Suppose P(X = 0,Y = 0) = 1/3, P(X = 0, Y = 3) = 1/3, and P(X =

6, Y = 3) = 1/3. Find Cov(X, Y) and the correlation p of X and
Y.

Answer 1

To find the covariance, use the formula Cov(X, Y) = E(XY) - E(X)E(Y). The correlation cannot be determined without standard deviations.

Step-by-step explanation:

We can find the covariance, Cov(X, Y), using the formula:

Cov(X, Y) = E(XY) - E(X)E(Y)

First, we need to calculate the expected value, E(X), and the expected value, E(Y). Given the probability values, E(X) = 2, E(Y) = 1, and E(XY) = 2*1/3 + 6*1/3 = 4/3.

Substituting the values into the formula, we get Cov(X, Y) = 4/3 - 2*1*1 = 1/3.

To find the correlation, we can use the formula:

p = Cov(X, Y) / (SD(X) * SD(Y))

Since the standard deviations are not provided, we cannot determine the correlation without further information.