UC Merced Rayleigh Distribution Advanced Probability Statistics Worksheet

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fgriroelnag2020

Mathematics

University of California Merced

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х Suppose X1...X, is an independent and identically distributed sample. It is a Rayleigh distribution with parameter 0 > 0 and its pdf can be found from: -x/ 021 x) x > 0. (a) Show E(X) = using integration by parts knowing .(-e * = fo(t) = 2 *°1203 o 2 that * (- e**(20) = f,(x) and that integrating the right half of the distribution gives d dx = MM you 0.5. (b) Determine Omm , the method of moments estimator. (c) Determine l(e), the log-likelihood function. (d) Determine Omle , the MLE. To do this, s=eto reparametrize l(0). use
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