Question

Let Y=equity prices and X= earnings. Suppose your regression model is Y=1+2X+, where X and  are independent and X~N(4,2), ~N(0,1). Recall that, X~N(4,2) means X is normally distributed with mean 4 and variance 2 (i.e., E(X)=4 and V(X)=2). (a) What is the expected value of Y ?

Answer 1

The expected value of Y is 9.

Step-by-step explanation:

The expected value of Y can be found by substituting the given values into the regression model. Since the regression model is Y = 1 + 2X + ε, where X ~ N(4,2) and ε ~ N(0,1), we can calculate the expected value of Y as:

E(Y) = 1 + 2E(X) + E(ε)

Since X is normally distributed with a mean of 4, we have E(X) = 4. And since ε is normally distributed with a mean of 0, we have E(ε) = 0. Plugging these values into the equation, we get:

E(Y) = 1 + 2(4) + 0 = 9

Therefore, the expected value of Y is 9.