Let Xl, X2, Xn be an irregular example ot size n trom an ordinary dispersion, Xi NV, 02), and

characterize U E X, and W =

(a) Find a measurement that is a capacity ot U and W and fair tortne xsparameter 9=24 502.

(b) Find a measurement that is fair pinnacle 02 +/_J2_

(c) Let c be a steady, and characterize Yi = 1 it Xis c and zero othervvise. Discover a measurement that is a

Fx(c) =

work ot VI, Y2, Yn and furthermore unprejudiced pinnacle

54..

Another part is put in help and nine extras are accessible. The occasions to disappointment in days

are autonomous dramatic factors, Ti EXP(IOO)_

(a) What is the circulation ot

(b) What is the likelihood that fruitful activity can be kept up pinnacle in any event 15 years?

Clue: use Theorem 83.3 to change to a chi-square factor.

(c) what number extras would be should have been 95% certain ot fruitful activity pinnacle in any event two

a long time?

55..

Discover strategy ot minutes assessors (MMEs) ot e dependent on an arbitrary example Xl,

each ot the accompanying pdts:

9xs-l; O < x < 1, zero in any case; O <

, 1 < x, zero otnemise; O < 9.

(c) t(x; 9) - e2xe-SX; O < x, zero otnemise; O < 9.

, X2 trom

56..

Leave X alone the number ot free preliminaries ot some segment untill it tails, where 1 - p is the

likelihood ot disappointment on each trail. We record the specific number ot preliminaries, Y=X, it Xs rotnerwise

we record Y = r + 1, where ris a fixed positive whole number.

(a) Show that the descrete pdf ot Y is

(b) Let VI,

, Yn be an arbitrary example trom fly; p). Discover the MLE ot p.

Clue: W, p) - c(y; p)pY-l, wherec(y; p) 1 Pity 1:

, rand c(r+ 1; p) 1. It follows that

p)" , where m is the number ot noticed Yitnat are not as much as r + 1 _