The dissemination work for X. the quantity of minutes an individual shows up sooner than expected for arrangements, is given beneath.

F(x).

a)

0

40 20x - x2 - 40 60 1

x < 0 < x < 4

4 < x <10

x > I 0

The goal is to diagram the circulation work. To dothis, place F(x) on the upward pivot, and the X qualities on the level hub. Coming up next is the circulation work plot.

"'

Dissemination Function Plot

O

N 0

O

O

0

2

4

x

6

8

10

b) The goal is to discover the likelihood that the individual shows up at any rate 5 minutes ahead of schedule for an arrangement. To discover this likelihood, ascertain P(X 5) = I - P(X <5) as follows. 1P(X < 5) = F(5) 20(5)- 5' - 40 - 1 60

35 60 = 0.417 There is 41.7% of chance for an individual to show up at any rate 5 minutes ahead of schedule for the arrangement.

c) The goal is to discover the likelihood thickness capacity of X. To dothis, take the subsidiary of the conveyance work. 0 x<0 2 ( x 0 < X < 4 dx 40 d 20x - x2 - 40) 60 4 <\-.10 dx x >10 dx 0 x < 0

f(x) =

(20) (20 - 2x) 60

0 x 4

4 5. x 10

Subsequently, the likelihood thickness capacity of X is given by

(x)

x 20' 10 - x

30

0 < x < 4

4

2--------------

A firm has been checking its absolute day by day phone utilization. The day by day utilization of time adjusts to the accompanying likelihood thickness work (estimated in hours).

32(4 ), 0 < x < 4 f (x) = 0, in any case

a Graph the likelihood thickness work. b Find the appropriation work F(x) for day by day phone utilization X . c Find the likelihood that the time phone utilization by the firm will surpass 2 hours for an arbitrarily chosen day. d The current financial plan of the firm covers just 3 hours of every day phone utilization. How frequently will the planned figure be surpassed?

3------------------

The pH level, a proportion of sharpness, is significant in investigations of corrosive downpour. For a specific lake, pattern estimations of acridity are made so that any progressions brought about by corrosive downpour can be noted. The pH for water tests from the lake is an arbitrary variable X with likelihood thickness work

f (x) =

Ilil (7 x)2, 5 < x < 7 0, in any case.

a Sketch the bend of f (x). b Find the circulation work F(x) for X . c Find the likelihood that the pH for a water test from this lake will be under 6. d Find the likelihood that the pH of a water test from this lake will be under 5.5 given that it is known to be under 6.

4------------

The extent of time during a 40-hour week's worth of work that a mechanical robot was in activity was estimated for countless weeks. The estimations can be displayed by the likelihood thickness work

f (x) =

2x, 0 < x < I 0, in any case.

On the off chance that X means the extent of time this robot will be in activity during a coming week, track down the accompanying. a P(X > 1/2) b P(X > 1/2 1 X > 1/4) c P(X > 1/4 1 X > 1/2) d F(x). Chart this capacity. Is F(x) consistent?