Probability

Maximum likelihood estimation

The random variables X1,X2,…,Xn are continuous, independent, and distributed according to the Erlang PDF

fX(x)= (λ^3*x^2*e^(−λx))/2, for x≥0,

where λ is an unknown parameter. Find the maximum likelihood estimate of λ, based on observed values x1,x2,…,xn. Express your answer as a function of n and s where s=x1+x2+…xn.

^λML=

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  2. ^λML= (3*n)/s

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