Exercise 2.8 Suppose that y is discrete-valued, taking values only on the non-negative integers, and the conditional distribution of y given a is Poisson: j = 0, 1, 2 Pr(y=j|x)= (exp(- x' * beta) * (x' * beta) ^ j)/(j!)

Compute \mathbb{E} (y|x) and var (yx). Does this justify a linear regression model of the form y = x' * beta + e'

Hint: If Pr(y = j) = (exp(- lambda) * lambda ^ j)/(j!) then \mathbb{E}*y = lambda and var(y) = λ.