A transport shows up at a bus station at a haphazardly chosen time inside an I-hour term. A traveler

shows up at the bus station at a haphazardly chosen time around the same time. The traveler is

willing to sit tight for the transport for up to 1/4 of 60 minutes. I'Vhat is the likelihood that the traveler will

get the busl (Hint: Let X indicate the transport appearance time, and let Y signify the traveler appearance

time.) Ifthese arnvals are autonomous, at that point

1,

0,

Presently discover P(YX Y+ 1/4).

Osx

somewhere else.

50- -

A specific cheap food outlet is keen on the joint conduct ot the irregular variable X, which is

characterized as the absolute time: in minutes, between a client's landing in the cheap food outlet and his

or on the other hand her leaving the help window, and Y, which is the time that the client holds up in line previously

arriving at the assistance window. Since X incorporates the time that a client holds up in line, we should

have X 2 Y. The relative recurrence dispersion of noticed upsides of X and Y can be demonstrated

by the likelihood thickness work

x

o,

a Find Y > 1).

b Find 2Y).

for 0 S y x < 00

somewhere else.

c Find the peripheral thickness work pinnacle the complete holding up time X

d Find the contingent thickness work oftotal holding up time since its getting late spent holding up in line

prior to arriving at the help window.

51 -

For each pair of arbitrary factors, demonstrate whether it is fitting to register the

relationship.

a Time went through concentrating every week (60 minutes, 2 hours,

10 hours) and grade (A, a, C, D, F)

b Educational accomplishment (grade school, secondary school, some school, school and postgraduate

preparing) and compensation S20,ooo, S20,ooo to < $50,000, $50,000 to < OO,OOO, in any event Sl 00,000)

c airtn request (first youngster, second kid,

what's more, level ot extroversion (high, medium low)

d Weight and time to finih a 100-meter run

52 -

Bollworms (Heliothjs spp.) are an irritation of cotton that cause financial harm if uncontrolled. Woman

scarabs (Hippodamja convergens) are characteristic bugs of bollworms. In the event that adequate quantities of woman

creepy crawlies are available in a specific cotton field, at that point substance control may not be required. Let X

also, Y mean the quantities of bollworms and woman insects on a cotton plant, separately. A

scientist investigated the relationship in these t',vo factors in a cotton field and found that they

had the accompanying joint appropriation:

x

o

1

2

3

o

0.03

O. 04

0.09

0.12

1

04

0.05

0.07

0.10

2

0.11

0.09

0.06

0.01

3

0.10

0.06

0.02

0.01

a Find the mean number of bollworms on the plants in this cotton field.

b Find the mean number ot woman insects on the plants in this cotton field.

c Find the covariance between the numbers ot woman bugs and bollworms on a cotton plant.

d Find the connection between's the quantities of woman insects and bollworms on a cotton plant.