Assume that an appropriation work has the structure

0,

x2 + 0.1,

x,

1,

o < x < 0.5

0.5 < x < 1

a Describe Fl(x) and F2(x), the discrete and consistent parts ot F(x).

b Write F(YO as

clFl(x) + czF2(x).

d Find the normal worth ofthe arbitrary variable whose circulation work is F(x).

38 -

The span X of calls getting through a mobile phone is an arbitrary variable whose

dissemination work is

x/3

o,

2

1

1

where [y] means the best number not exactly or equivalent to y.

a Sketch F(x).

b Find 6).

c Find 4).

d Describe the discrete and ceaseless parts that make up F(x).

e Find E(X).

39 -

The "on" temperature ot a thermostatically controlled switch peak a cooling framework is set

at 72?F, however the real temperature X at which the switch turns on is an irregular variable having

the likelihood thickness work

1

71 < x < 73

0, in any case.

a Find the likelihood that a temperature in overabundance of 72?F is needed to turn the svvitch on.

b If such switches are utilized autonomously, discover the likelihood that a temperature in abundance

of 72?F is needed to turn both on.

40 - ----

Allow X to have a thickness work

X C.r2,

o,

a Find c.

b Find FOO.

c Grapn f (x) and F(x).

somewhere else.

d use F(x) trom part (b) to discover a-I), F(I), and F(l).

e Find

f Find the mean and the change ofX.