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Part III - Maximum Likelihood Suppose X1, . . . , Xn is a random sample from the following density r s 2π exp{−s/(2X)} X3/2 f(X|s) = I(X > 0), where s is an unknown parameter. 10. What is the log-likelihood function? 11. Suppose we want to numerically calculate the MLE of s using Newton’s method. Write a program to do this and run your program starting from 0.1. 12. Let sˆ be the MLE obtained above. Construct an approximate 95% confidence interval for s, centered at sˆ.

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