Leave X and Y alone together disseminated irregular factors with limited differences.

a Show that [E(XY)? < E(X?)E(?). (Clue

E[(tX Y)?] = 0; or equally,

?PE(X?) 2tE(XY) + E(Y') = 0.

This is a quadratic articulation of the structure At? +Bt +C, and on the grounds that it isn't negative, we should

have B? - 4AC < 0. (The first disparity follows straightforwardly.)

_ cov(X, Y)

P= VO)

Utilizing the disparity of section (a), show that 92 < 1

66 -

Let X;, X,.....X;, be autonomous arbitrary factors with E(x) = y and V(X) = 0, for i= 1, 2.

rn Let

n

U= So aX

i=l

What's more,

a

Un =o iX;

i=l

where ay, a>, an and by, bp, ... , Oy are constants. U, and U are supposed to be symmetrical if

n

Cov(Uy, Us) = 0. Show that Uy and Uz are symmetrical and onyit ). azbj = 0.

i=1

67 -

'The middle yearly pay for heads of families in a specific city is $52,000. Five such heads

of family are haphazardly chosen for consideration in an assessment of public sentiment. Leave X alone the number (out of

the five) who have yearly wages underneath $52,000.

a Give the likelihood conveyance of X

b Define Y,, the number (out of the five) who have yearly wages of in any event $52,000, as a

capacity of X

Find the likelihood capacity of

68 -

The representatives of a firm that does asbestos cleanup are being tried for signs of asbestos

in their lungs. The firm is approached to send four representatives who have positive signs of

asbestos to a clinical place for additional testing. Assume 40% of the representatives have positive

signs of asbestos in their lungs. Leave X alone the quantity of representatives who don't have

asbestos in their lungs tried prior to tracking down the four who do have asbestos in their lungs.

'a Give the likelihood work for X

b Let Ybe the all out number of representatives tried to discover four with positive asbestos in their lungs.

Characterize Yas an element of X

Find the likelihood capacity of