# 4. (a) The density of a Poisson (-1) random variable is f1(y;) = t4e-1/ Use this...

###### Question:  4. (a) The density of a Poisson (-1) random variable is f1(y;) = t4e-1/ Use this density to find the MLE for and the MLE for u = 1-1. Hint: you might want to find the MLE for u first, and then apply the principle of invariance to find the MLE for 1. (b) Find the MLE for u = 1-1 using the original sample of waiting times and the principle of invariance of the MLE. Do you expect your answer to be exactly the same as your answer to part (a)? Why or why not? 111
6. (a) Compute a 95% confidence interval for p using its asymptotic distribution, that is, its distribution for large n, using the observed values of the random sample Y1, ... ,Ym. (b) It can be shown that the asymptotic distribution related to the MLE for is Compute a 95% confidence interval for using this asymptotic distribution of the MLE and the observed values of the random sample X1, ..., Xn. (c) Compare your confidence intervals in part (a) part (b). Interpret both of them: that is, “we are 95% confident that is between and ." Remember that Mo = o.

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