- #1
twoski
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Homework Statement
Given f(x;λ) = [itex]cx^{2}e^{-λx}[/itex] for x ≥ 0
Determine what c must be (as a function of λ) then determine the maximum likelihood estimator of λ.
The Attempt at a Solution
So I'm supposed to integrate this from 0 to infinity, from what i can gather.
Let u = [itex]x^{2}[/itex], du = 2xdx, dv = [itex]e^{-λx}[/itex] and v = [itex]-e^{-λx} / λ[/itex]
After a bit of work i end up with:
-c/λ [ [itex]x^{2}e^{-λx}|_{0}^{∞} + 2( xe^{-λx}/λ |^{∞}_{0})[/itex] ]
What throws me off is that evaluating this leaves me with -c/λ( 0 ), which has to be wrong...