A framework is formed ot five autonomous segments associated in arrangement.

(a) It the pdf ot the opportunity to disappointment ot every part is remarkable, Xi EXP(I), then, at that point give the

pdf ot the opportunity to disappointment ot the framework.

(b) Repeat (a), yet accept that the parts are associated in equal.

(c) Suppose that the five-part framework tails when at any rate three segments tail. Give the

pdf ot the opportunity to talure ot the framework.

(d) Suppose that n free segments are not circulated indistinguishably, yet rather Xi

Exhibition. Give the pdf ot the chance to disappointment ot an arrangement framework for this situation.

50..

Considera irregular example ot size n trom a circulation witn CDF F(x) 1 - x-2 f x > 1, and

otnemise. Decide if each ot the accompanying arrangements nas a restricting circulation; it thus,

then, at that point give the restricting conveyance.

(b) xmn.

- 1/2xn:

51..

A particular kind ot weapon nas likelihood p ot working effectively. We test n weapons, and the

reserve is supplanted it the number ot talures, X, is at any rate one. How huge must to be to nave

hatchet 2 1] 0.99 wnenp 0.95?

(a) utilization accurate binomial.

(b) utilize typical estimate.

(c) Use Poisson approximatiom

(d) Rework (a) through (c) witn p

- 0.90.

52..

Consider an irregular example trom a Poisson dispersion, Xi POI(u).

(a) Show that y. e-* meets stochastically to RX=OI e-u.

(b) Find the asymptotic typical appropriation ot Yn.

(c) Show that exp meets stochastically to PIX