Let X and Y nave a joint dissemination that is unfirm over the three-sided locale in the

going with graph.

a Find the minor thickness of Y.

b Find the minimal thickness of X.

c Find the restrictive thickness work ot Y given X.

d Find Y) 0].

62 -

Allow X to have a mathematical circulation; that is: let

p(x) = p)X,

The objective is to discover V(X) through a contingent contention.

a Let Y = 1 if the main preliminary is a triumph, and let Y = 0 if the primary preliminary is a disappointment. Contend that

E(x21Y = 1) O

E(x21Y = 0) = + x )2].

Compose E(X2) as far as E(X21Y).

Improve on the articulation to some extent (b) to show that

d snow that

63 -

Leave X alone a persistent arbitrary variable with appropriation work F(x) and thickness work f (x).

We would then be able to compose for

p(x) = p)X,

As an element of x2 pinnacle fixed xl, the right-hand side ot this articulation is known as the restrictive

appropriation capacity of X, given that X 2 xl. On taking the subsidiary regarding x2, we see

that the comparing contingent thickness work is given by

E(x21Y = 1) O

E(x21Y = 0) = + x )2].

Assume that a specific kind ot electronic part has life length X with the thickness work

(light length estimated in hours)

2

Track down the normal length ot life for a segment of this kind that has effectively been being used pinnacle 100

hours.

64 -

Let X;, X, and X3 be arbitrary factors, either ceaseless or discrete. The joint second

creating capacity of X;, Xp, and X; is characterized by

_ 1X1 4+12X2413X3

M (t, (2,13) = Ele )-

a Show that M(t,, t, t3) gives the occasion creating capacity for Xj + Xp +X,

b Show that M(t, f, 0) gives the occasion producing capacity for X1 + X2.

Show that

aki +o+8s M (1, t,13)

=E (x1'x22x2) .

att! ak ary? pees

t=h=h=0