Question

1,2,4

Comment An equivalent expression for n (1/) sequence of This provides a very convenient conting formala. Accumulating mana of Smuch easier tod a y cakulator than com ting sums of squares of differences Rougemors will also tend to be a problem with this second formation es, though sed in that ust Epidemiologists at a county hospital ospital located at a clear waste disposal mo h anlal Chronic leuke The number of patients ang into that category for the past 12 years were 2. 0.0.1.1.1. 1.0 and sume that the occurrence of such patients per year he described by a Poisson pdl. Estimate the relevant parameter in Example 5.4.1) a 541 Let Y Y be a random sample from any nder what conditions is the estimator whose mean is W - MYY..... YJ- 4, unbiased ? 43 Find an unbiased estimator for Bused on the smallest of order statistics drawn from a uniform distribution defined over s 5.4.4 A drug reaction surveillance program was carried out in mine major hospi- als (105L Out of a total of 11.536 patients monitored it was found that 3240 experienced some form of adverse reaction to their medication. What mathematical model applies to these data? Estimate the relevant parameter. Is the estimator on which your estimate is based, unbiased Question 545 Suppose that 14, 10, 18, and 21 constitute a random sample of size four drawn from a uniform pdf defined over the interval (0 ) where is unknown. Find an expression for an unbiased estimator for 8 based on Y, the third order statistic Evaluate the estimator using the data given. Is it possible that an estimate based on Y's would be clearly inappropriate in a given situationExplain. Question 5.46 A student takes a freshman chemistry exam that the professor claims has always resulted in approximately normal distributions when he has given the test in the past. If the student makes a grade of 66, estimate the class average Question 5.4.7 Let w, and w, be any two unbiased estimators for the parameter 0. If W- W, + bw, is also to be an unbiased estimator for B, what must be true of a and b? Chap 5 Sec. 5.4 Unbiasedness

Answer 1

PAGF Dear student if you are satisfied please THUMBS Qup. 15.4.1 Data 2, 1, 0, 0, 1, 1, 1, 4, 1, 0, 2, 3 if x follows Poisson distribution Tie, fcx)=eta N=0, 1, 2,... ali the unknown where 7 is parameter. We have estimator a = ă is an unbiased for unknown parameter z is the sample mean. where x as an So here we estimator can use for a.

się z Tc = x [2+1+0+...+2+3) since Y, Y2,... Yo are random sample, they are identically and iden pendently distributed which means, EC Yi) = H for all i=1,200.0 as à = 4 = 103333 is an Here, we want Ę Cai Yi) = pl. 11 estimate for a 5.4.2 W = b (Y,..., Yn) = 2 any; We want to find an unbiase estimator for fe where. He is the polution mean » 2 có 2 (Y) = 1 & ai M = M. ai = 1 #1=1,2,...n. 려

5.44 2 2 e la polidas LY : is an unbiased. estim ator of fione Since, We can use Binomial model in this data vil lg x~ Binomial (n, P). Here n = 11526, but bis Unknown enoto ofl. n M. For binomial distribution | Sapa P70 205 6top P = x which is an unbiased estimator for 'population proportion p : = 82.4-0 - 0:2811 03sRI is an unbiased estimator for P. Tel . * £ Y; = ï is an unblosed estimator for me. 11526

unbiased ness proof.. if y a Binomial Chip) then Ę (x) = npath Hos C Ô ) = p. 914 so Ô ſe an unbiased estimator of P.