Math Problem Statement

есть результаты трех независимых наблюдений 2, 3, 1 случайной величины X, имеющей распределение Пуассона с параметром λ>0\lambda>0. Найти оценку максимального правдоподобия для P(X=0).

Solution

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Math Problem Analysis

Mathematical Concepts

Poisson Distribution
Maximum Likelihood Estimation (MLE)
Probability Theory

Formulas

Poisson Probability: P(X = k) = (λ^k * e^(-λ)) / k!
Likelihood Function: L(λ) = Π (λ^x_i * e^(-λ)) / x_i!
Log-Likelihood Function: ln L(λ) = Σ (x_i ln λ - λ)

Theorems

Maximum Likelihood Estimation

Suitable Grade Level

Undergraduate/Graduate Level (Statistics or Probability Theory)