Math Problem Statement

Let X1,· · · , Xn be a random sample from a Poisson distribution with parameter λ, i.e., f (x) = λxe λ x! , x = 0, 1, . . . Find the MLE of the parameter λ.

Solution

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Math Problem Analysis

Mathematical Concepts

Maximum Likelihood Estimation
Poisson Distribution
Statistical Estimation

Formulas

Likelihood function: L(λ) = ∏(λ^xi e^−λ / xi!)
Log-likelihood function: ℓ(λ) = Σ(xi) log(λ) − nλ
MLE for λ: λ̂ = (1/n) Σ(Xi)

Theorems

Maximum Likelihood Estimation

Suitable Grade Level

Undergraduate Statistics