Suppose that Y is discrete valued, taking values only on the non negative integers, and the conditional distribution of Y given X x is Poisson P Y j X x exp( xB)(x) j j 0,1,2, Compute E YIX and var Y X Does this justify a linear regression model of the form Y X' e then E Y and var Y 1 Hint If P Y j exp( 1)j

Question: Suppose that Y is discrete-valued, taking values only on the non-negative integers, and the conditional distribution of Y given X x is Poisson: P[Y=j|X=x]=

Suppose that Y is discrete-valued, taking values only on the non-negative integers, and the conditional distribution of Y given X Æ x is Poisson: P[Y=j|X=x]= exp(-xB)(x) j! j=0,1,2,... Compute E[YIX] and var [Y | X]. Does

P[Y=j|X=x]= exp(-xB)(x) j! j=0,1,2,... Compute E[YIX] and var [Y | X]. Does this justify a linear regression model of the form Y = X'+e? then E[Y] and var [Y] = 1. Hint: If P Y j]= exp(-1)j

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