3. Let X₁, X2, Xn represent a random sample from a Rayleigh distribution with proba- bility density function given below. X f(x) == ex²/(20), x>0 е (a) Show that E(X²) = 20. Look up 1²-¹e-¹ dt. (b) Find E (1X) and hence find an unbiased estimator of 0. (c) Estimate from the following observations using the estimator found in part (b). the gamma function, I'(z) = 16.88 10.23 4.59 6.66 13.68 14.23 19.87 9.40 6.51 10.95
3. Let X₁, X2, Xn represent a random sample from a Rayleigh distribution with proba- bility density function given below. X f(x) == ex²/(20), x>0 е (a) Show that E(X²) = 20. Look up 1²-¹e-¹ dt. (b) Find E (1X) and hence find an unbiased estimator of 0. (c) Estimate from the following observations using the estimator found in part (b). the gamma function, I'(z) = 16.88 10.23 4.59 6.66 13.68 14.23 19.87 9.40 6.51 10.95
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:3. Let X₁, X2, Xn represent a random sample from a Rayleigh distribution with proba-
bility density function given below.
...9
X
f(x) = -=- e – x² / (20)
Ө
(a) Show that E(X²) = 20.
Look up the gamma function, I(z) = f*
9
x > 0
t²-¹e-t dt.
(b) Find E (Σ½-1 X²) and hence find an unbiased estimator of 0.
i=1
(c) Estimate from the following observations using the estimator found in part (b).
16.88 10.23 4.59 6.66 13.68
14.23 19.87 9.40 6.51 10.95
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