Find a sufficient statistic for the Rayleigh density, f

Chapter , Problem 73

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QUESTION:

Find a sufficient statistic for the Rayleigh density,

                                         \(f(x \mid \theta)=\frac{x}{\theta^{2}} e^{-x^{2} /\left(2 \theta^{2}\right)}, \quad x \geq 0\)

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QUESTION:

Find a sufficient statistic for the Rayleigh density,

                                         \(f(x \mid \theta)=\frac{x}{\theta^{2}} e^{-x^{2} /\left(2 \theta^{2}\right)}, \quad x \geq 0\)

ANSWER:

Step 1 of 2

The density function for the Rayleigh distribution for random variable ;

, and  

The function  follow as;

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