# Baysian calcul: Consider the density f(x|λ) = 1/λ*exp(−x) for x ≥ 0.

#### fly

##### New member
Baysian calcul: Consider the density f(x|λ) = 1/λ*exp(−x) for x ≥ 0.

Consider the density f(x|λ) = 1/λ*exp(−x) for x ≥ 0.

1) If the prior for λ ≥ 1 is uninformative i.e. π(λ) ∝ 1 what is the
posterior ? Is it proper ?
2) If the prior for λ ≥ 1 is π(λ) ∝ λ^(−2) what is the posterior ? Is it
proper ? Does it admit an expectation ? Does it admit a variance ?

I use the Bayes formula:

1) π(λ/x)= f(x|λ)*π(λ) / f(x) and i find π(λ/x)=exp(-x) for x positive

2) but for the second question, i find the same distribution function, does it correct? I think something is wrong with my calcul.