The prior \lambda is distributed according to \textsf{Exp}(a) (a > 0). Write the probability distribution function \pi (\lambda ), in terms of \lambda and a. Do not simplify.

Question

\pi (\lambda )=
Our expression for \pi (\lambda ) uses two variables.

Which one may be ignored (in the context of the problem) if it is used as an outermost multiplier in the expression written in proportional notation?

a

\lambda

Both a and \lambda

Write the simplified expression for \pi (\lambda ), ignoring the parameter(s) chosen earlier when used as an outside multiplier.

Hint: Your resulting expression for \pi (\lambda ) would satisfy \pi (0)=1 regardless of the value of a.

\pi (\lambda )=

Suppose that instead of it being an outermost multiplier, it plays a different role in the formula. Which of the following statements are true?

It may still be ignored if the parameter is added to the expression.

It may still be ignored if the (nonzero) parameter is divided from the expression.

It may still be ignored if the expression is taken to the power of the parameter.

Answer 1

If a is used as an outermost multiplier in the expression, it may still be ignored if the parameter is added to the expression.

If a is added to the expression, it may still be ignored.

If a is divided from the expression, it may still be ignored.

If the expression is taken to the power of a, it may still be ignored.