Question

236 Some Statistical Inferences the histogram. Use the R function dganna(X, 8hape. 1,scale-のto evaluate the plf. (c) Obtain the sample median of the data, which is an estimate of the median lifetime of a motor. What parameter is it estimating Le., determine the nedian of x)? (d) Based oa the mle, what is another estimate of the median of X? .1.2. Here are the weights of 26 professional baseball pitche; see page 76 of Hettmansperger aad McKean 2011) for the complete data set]. The data are in R file bb.rda. Suppose we assume that the weight of a professioal baseball pitcher is normally distributed with mean and variance ơ2 160 175 180 185 185 185 190 190 195 195 195 200 200 200 200 205 205 210 210 218 219 220 222 225 225 232 a) Obtain a histogram of the data. Based on this plot, is a normal probability (b) Obtain the maxinnin likelihood estimates of μ. σ2, o, and μ/o. Locate your nodel credible? estimate of A on your plot in part (a). Then overlay the ormal pdf with these estimates on your histogram in Part (a). (c) Using the binonial model, obtain the maxinun likelibood estimate of the proportion p of professional baseball pitchers who weigh over 215 pounds (d) Determine the mle of p assuning that the weight of a professional baseball player follows the i rial probability model N(a.o2) with μ and σ unknown. 4.1.3. Suppose the uumber of customers X that enter a store between the hours 9:00 a.m. and 10:00 a.m. follows a Poisson distribution with parameter . Suppose a random sample of the umber of custoaners that enter the store between 9.00 a.m and 10:00 a.m. for 10 days results in the values 9 79 15 10 13 11 7 2 12 (a) Determine the maxin likelihood estimate of 8. Show that it is a unbiased (b) Based on these data, obtain the realization of your estimator in part (a). estimator Explain the meaning of this estimate in ters of the number of customers. 4.1.4. For Example 4.1.3, verify equations (4.1.4) 4.1.8) 4.1.5. Let Xi, X2...Xn be a randon sample froan a continuous-type distribution. (a) Find P(XI-Xy), P(X1S X2.x1S Xa) , P(X1S Х,,i-2.3, .. .. n).

Can you solve Question 4.1.3 with details? This is from Advanced Statistics.

Answer 1

The mean number of customers enter a store between the hours 9.00 am and 10.00 am is 9.5.