Unformatted text preview: 5. (Invariance Principle) If ˆ θ 1 , ˆ θ 2 are the MLE’s of θ 1 , θ 2 , the MLE of h ( θ 1 , θ 2 ) is h ( ˆ θ 1 , ˆ θ 2 ) . Inclass problems Example 6.15. Example 6.16. Example 6.21. Exercise 6.25. Assuming normal distribution, find c such that P ( strength ≤ c ) = 0 . 95 . > x<strength > length(x) [1] 10 > sd(x) [1] 19.87852321 1 2 3 0.0 0.1 0.2 0.3 0.4 y dnorm(y) Figure 1: Density of N (0 , 1) > sigma<sqrt((length(x)1)/length(x))*sd(x) > sigma [1] 18.85842 > qnorm(0.95,mu,sigma) [1] 415.4193 > qnorm(0.95) [1] 1.644854 > pnorm(415,mu,sigma) [1] 0.9476644 > y< 30:30/10 > plot(y,dnorm(y),’l’) Selfstudy problems Example 6.17., Example 6.18., Exercise 6.23., Exercise 6.29....
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 Fall '04
 Chung
 Statistics, Normal Distribution, Probability, probability density function, Maximum likelihood, Estimation theory, Likelihood function, maximum likelihood estimation

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