The LJ.S. Enumeration Bureau gathers data on specific qualities in the LJ.S. populace.

For 2004, it announced the accompanying quantities of residents by age and whether they were in

poveny as demonstrated in the smearing table (all includes are in 1000s ot individuals).

Age (in years)

Under 18

18 to 64

65 and more seasoned

Aggregates

Live in Poverty

347

517

130

994

Try not to Live in Poverty

12,680

19,997

3,327

36,004

Tota

13,0

20,5

36,9

Assume an individual is chosen aimlessly from the residents ot the United States and their age

furthermore, destitution status are noticed. Let X, the arbitrary variable related with age, and Y, the

irregular variable addressing poveny status, be characterized as follows:

x

Furthermore,

9,

41,

82,

O,

1,

on the off chance that age < 18

on the off chance that 18 < age < 64

on the off chance that age 65

if not living in neediness

in the case of living in destitution.

a Find the joint likelihood circulation of X and Y.

b Find the minimal likelihood dispersion old enough.

c Find the minimal likelihood dispersion of destitution in the United States.

46 -

A radioactive molecule is arbitrarily situated in a square region witn sides that are 1 unit long. Let

X and Y indicate the directions of the molecule. Since the paicle is similarly liable to fall in any

subarea of fixed size, a sensible model of (X, Y) is given by

1,

0,

Osxsl, 0 sy sl

somewhere else.

a Sketch the likelihood thickness surface.

b Find 0.2, 0.4).

c Find Pro. 1 s X 0.3, Y >

47 -

A natural architect estimates the sum (by weight) of particulate contamination in air

tests (of a specific volume) gathered over the smokestack of a coal-filled force plant. Let X

indicate the measure of toxin per test when a specific cleaning gadget on the stack isn't

working, and let Y indicate the measure of poisons per test when the cleaning gadget is

working under comparable natural conditions. It is seen that X is consistently more noteworthy than 2Y,

what's more, the overall recurrence of (X, Y) can be displayed by

k,

0,

Osx<2, 0 s y s l, 2ysx

somewhere else.

(At the end of the day, X and Yare arbitrarily dispersed over the area inside the triangle limited by

x 2, y O, and 2y=x.)

a Find the worth of k that makes this a likelihood thickness work.

b Find P(X2 3Y). (All in all, discover the likelihood that the cleaning gadget will decrease the

measure of contamination by 1/3 or more.)

48 -

A youngster readies a combination of peanut butter, bananas, and jam peak his school lunch every day. Let X

furthermore, Y signify the extents ot peanut butter and bananas, individually. The combination

extents shift from one day to another as indicated by the joint likelihood thickness given by

50,

o,

0.4 0.6, 0.10 0.30,

something else.

For an arbitrarily chosen day, discover the likelihood ofthe blend having the accompanying

attributes.

a The extent of peanut butter is under 1/2 and the extent of bananas is under 1/6.

b The extent of peanut butter is under 1/2 and the extent ot bananas is more noteworthy than

c The extent of peanut butter is under 1/2.

d The extent of peanut butter is more noteworthy than I given that the extent of bananas is

more noteworthy than If.