We will use proportionality notation in order to simplify the Gamma Distribution. But first, we perform a cosmetic change of variables to avoid repetitive notation with our answer in Part I: we write our parameters instead as \lambda _0 and q_0.

Question

From the expression for the Gamma distribution given above, remove outermost multipliers to simplify it in such a way that our expression for f(1) is e^{-\lambda _0} regardless of the value of q_0.

Use q_0 for q_0 and lambda_0 for \lambda _0.

f(x) \propto

Answer 1

x^{q_0-1}e^{-\lambda_0 x}