Recitation 9 Solutions

Recitation 9 Solutions - Steven Weber Dept. of ECE Drexel...

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Steven Weber Dept. of ECE Drexel University ENGR 361: Statistical Analysis of Engineering Systems (Spring, 2010) Recitation 9 Solutions Question 1. Let X 1 ,...,X n represent a random sample from a Rayleigh distribution with pdf f ( x ; θ ) = x θ e - x 2 2 θ , x > 0 . (1) Please do the following: 1. It can be shown that E [ X 2 ] = 2 θ . Use this fact to construct an unbiased estimator of θ based on X 2 i . Show that it is unbiased. ˆ θ = X 2 i 2 n , E [ ˆ θ ] = 1 2 n E [ X X 2 i ] = 1 2 n n X i =1 E [ X 2 i ] = 1 2 n n X i =1 θ = θ. (2) 2. Estimate θ from the following n = 10 observations on vibratory stress of a turbine blade under specified conditions: 16 . 88 10 . 23 4 . 59 6 . 66 13 . 68 14 . 23 19 . 87 9 . 40 6 . 51 10 . 95 . (3) 16 . 88 2 + ··· + 10 . 95 2 = 1490 . 1058 , ˆ θ = 1490 . 1058 2 · 10 = 74 . 505 . (4) www.ece.drexel.edu/weber 1 May 28, 2010
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Recitation 9 Solutions - Steven Weber Dept. of ECE Drexel...

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