Question

Suppose you are part of the analytics team for the online retailer Macha Bucks which sells two types of tea to its online visitors: Rouge Roma (RR) and Emerald Earl (EE). Everyday approximately 10,000 people visit the site over a 24 hour period. For simplicity suppose we consider the “buy one or don’t buy” (BODB) market segment of customers which when they visit the site will conduct one of the following actions: (a) buy one order of RR, (b) buy one order of EE, or (c) don’t buy (DB) anything. You have been tasked with determining customer behavior on the website for the BODB segment using a random sample of 35 visits.

In the dataset for the random sample, each row corresponds to a random visitor. For each visitor we provide both the visitor’s action as well as the profit earned on the transaction. In the action column:

if the visitor buys one order of RR, we see a RR,
if the visitor buys one order of EE, we see an EE,
if the visitor doesn’t buy anything, we see a DB.

Note that even if two customers buy the same product, the profit can differ due to the shipping costs, promotions, or coupons that are applied

Random Sample of Data

1=yes, 0 = no

Transaction ID

Action

Profit ($)

Bought RR?

Bought EE?

Didn't Buy?

Profit RR ($)

Profit EE ($)

1

RR

8.43

1

0

0

.

0.00

2

DB

0.00

0

0

1

0.00

0.00

3

EE

1.75

0

1

0

0.00

1.75

4

DB

0.00

0

0

1

0.00

0.00

5

EE

4.37

0

1

0

0.00

4.37

6

EE

5.79

0

1

0

0.00

5.79

7

RR

6.27

1

0

0

6.27

0.00

8

RR

6.22

1

0

0

6.22

0.00

9

DB

0.00

0

0

1

0.00

0.00

10

EE

4.49

0

1

0

0.00

4.49

11

RR

10.54

1

0

0

10.54

0.00

12

EE

3.79

0

1

0

0.00

3.79

13

DB

0.00

0

0

1

0.00

0.00

14

DB

0.00

0

0

1

0.00

0.00

15

RR

9.03

1

0

0

9.03

0.00

16

EE

3.54

0

1

0

0.00

3.54

17

DB

0.00

0

0

1

0.00

0.00

18

DB

0.00

0

0

1

0.00

0.00

19

EE

5.02

0

1

0

0.00

5.02

20

DB

0.00

0

0

1

0.00

0.00

21

EE

3.60

0

1

0

0.00

3.60

22

DB

0.00

0

0

1

0.00

0.00

23

EE

2.61

0

1

0

0.00

2.61

24

RR

11.75

1

0

0

11.75

0.00

25

RR

12.22

1

0

0

12.22

0.00

26

DB

0.00

0

0

1

0.00

0.00

27

DB

0.00

0

0

1

0.00

0.00

28

EE

6.17

0

1

0

0.00

6.17

29

RR

8.83

1

0

0

8.83

0.00

30

DB

0.00

0

0

1

0.00

0.00

31

DB

0.00

0

0

1

0.00

0.00

32

DB

0.00

0

0

1

0.00

0.00

33

DB

0.00

0

0

1

0.00

0.00

34

RR

14.16

1

0

0

14.16

0.00

35

EE

6.06

0

1

0

0.00

6.06

PARTS

a) What could be an appropriate probability distribution to use for modeling the number of visitors that the website has in an hour?

b) What parameters would you use for the probability distribution?


c) Using that distribution, determine the probability that more than 600 people visit the site in an hour.

a) What could be an appropriate probability distribution to use for modeling the number of seconds between customer visits?

b) What parameters would you use for the probability distribution?


c) Using that distribution, determine the probability that the time between customer visits to the website is less than 10 seconds.

a) What could be an appropriate probability distribution to use for modeling the number of website visitors from 100 visitors that do not buy anything?

b) What parameters would you use for the probability distribution?


c) Using that distribution, determine the probability that from among 100 customers, it turns out that 30 or more customers do not buy anything.

d) What is the average number of visitors (from among 100 customers) that do not buy anything?

e) What is the standard deviation of the number of visitors (from among 100 customers) that do not buy anything?

What is the average profit from among 100 random customers that visit the site?
Please explain your answer or show your calculations.

Answer 1

a.. poisson distribution is an appropriate probability distribution to use for modelling the number of visitorsthat website he has in an hour

since arrival rate of customers visit the website follows poisson distribution

b. Arrival rate of customers follows poisson distribution with parameter ( lambda)

.= average no.of customers visit the website per hour =1000/24 = 416.666

c.probability that there is more than 600 customers visit the website in an hour

P( X>600) = 1- P( X<=600) =0 since P(X<=600) =1 where = 466.666/hour

a. An appropriate probability distribution use for modelling the number of secods between customer visits is an exponential distribution

since inter arrival time follows exponential distribution

b.inter arrival time follows exponential distribution with parameter 1/

c.from the given data we observe that interarrival time between the customers=1/ = 7.7142 seconds

  probability that the time between the customers visit the website is less than 10 seconds is given as

P(X<10seconds)= 0.72646 from exponential probability function

a. Appropriate probability distribution to use for modelling the no.of website customersfrom 100 visitors that do not buy any thing is poisson distribution

since the behaviour of the customers is indefinite

b. parameter of the distribution = = average no.of customers that do not buy any thing

= 1 since100 out of 100 customers that do not buy any thing

c. out of 100 customers 30 or more that do not buy any thing = P(X>=30) = 1- P( X<30) = 0

time out sorry