Leave X alone a r.v. indicating the lifetime ota certain part of a framework, and assume that X has

negative dramatic circulation with boundary A. Likewise, let the expense ot working this

piece of gear to time X = x.

(I) Compute the normal expense of activity over the lifetime ofthe segment under

thought, when:

(a) u, where c is a positive steady,

(b) c(l - 0.5e-'X), where a will be a positive steady.

(ii) Specify the mathematical qualities to some degree (I) when A 1/5, c-2, and a

= 0.2.

22..

The quantity of clients showing up at a help counter in a grocery store in a 5-minute time span is

a r.v. X which has Poisson conveyance witn mean 0.2.

(I) I'Vhat is the likelihood that the quantity of appearances in a given 5-minute time frame won't surpass 1?

(ii) It is realized that the holding up time betven two progressive appearances is a r.v. Y having negative

= 0.04 (L

dramatic circulation with boundary

l. Based on

this: what is the likelihood that the holding up time betven two progressive appearances is more than 5

minutes?

23..

A gum-ball machine gives out a red, a dark, or a green gum ball.

(a) Describe a suitable example space.

(b) List every conceivable occasion.

(c) It R is the occasion "red, " then, at that point list the results in R.

(d) It G is the occasion "green, then, at that point what is R n G?

24..

There are four fundamental blood gatherings: O, A, a, and Ad. Normally, anybody can get the blood ofa

contributor from their own gathering. Additionally, anybody can get the blood of a giver from the O bunch, and

any of the four kinds can be utilized by a beneficiary trom the Ad bunch.

Any remaining conceivable outcomes are unwanted. An investigation comprises of drawing a print ot blood and

deciding its sort for every one of the following two contributors vvho enter a blood donation center.

(a) List the conceivable (requested) results ot this examination.

(b) List the results relating to the occasion that the subsequent benefactor can get the blood of

the principal giver

(c) List the results comparing to the occasion that every benefactor can get that blood of the

other.