utilizing progressed grid hypothesis, t can be shown that the joint MGF ot a vector ot k-variate typical

arbitrary factors, X = (Xl, Xk), nas the torm given in Exercise 26, in particular M(tl, tk) = exp

[tp + (1/2)t'Vt] Witn p' = (VI, 'Jk) and . , tk). Accepting this outcome, snow the accompanying:

(a) The negligible dissemination ot every part is ordinary, X ,

ak) and b' 5k) and U = a'X and W= b'X, then, at that point U and Whave a bivariate

ordinary dissemination.

(c) U and Ware free if and just it a'Vb

68..

A segment in a repairable framework makes some mean memories to disappointment ot 100 hours. Five extra

segments are accessible.

(a) What is the normal activity time to be acquired?

(b) ltTi EXP(IOO) pinnacle every part and the five extras, what is the likelihood that the

framework will in any case be in activity atter 300 hours?

(c) what number extras are expected to nave a framework unwavering quality ot 0.95 at 300 hours?

69..

The disappointment time ot a specific electronic part follows a dramatic circulation, X

EXP(9). In an irregular example ot size n 25, one notices g = 75 days.

(a) Compute the MLE ot the unwavering quality at time g days, R(g)_

(b) Compute a fair-minded gauge ot R(g).

(c) Compute a 95% lower certainty limit peak R(g).

(d) Compute a 95% lower resilience limit peak extent 0.90.

70..

Expect that the number ot discharges ot particles trom a radioactive source is a homogeneous

Poisson measure Witn force 2 every second.

(a) What is the likelihood ot O discharges in 1 second?

(b) What is the likelihood ot O discharges in 10 seconds?

(c) What is the likelihood ot 3 discharges in 1 second?

(d) What is the likelihood ot 30 discharges in 10 seconds?

(e) What is the likelihood ot 20 discharges or less in 10 seconds?