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Competitive Stats
Q9Section I (Objective (Q1–Q80))9 of 80

Sufficient statistic — exponential distribution

Let x1,x2,…,xnx_1,x_2,\dots,x_n be a random sample from a distribution with p.d.f.

f(x,θ)={1θe−(x/θ);0≤x<∞0;otherwise.f(x,\theta)=\begin{cases}\dfrac1\theta e^{-(x/\theta)}; & 0\le x<\infty\\ 0; & \text{otherwise.}\end{cases}

The sufficient estimator of θ\theta is:

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