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Analysis of Data 2015-16

Quiz

Duration: 90 minutes

Maximum Marks: 30

Instructions:

1. This paper contains 3 questions. Answer all questions for full credit.

2. Quiz is open book, open notes and open computer. No communication device is permitted.

3. Answer only in the answer script in the space provided. We are not going to evaluate

anything that is not on the answer script.

4. Only the answer(s) appearing in the designated space in the answer script will be evaluated. Pleasedo not attach any rough sheets to the answer script as they will not be considered.

5. Brief reasoning may be included but there is no need to show work in detail, unless explicitly

asked for.

6. Question 1 requires you to provide reason for your answers, failing which you do not get any

credit for this question. For the rest of the questions you may choose to provide explanation for your

answers in the stipulated space, which may be considered for partial credit in the event your answer

is wrong.

7. All numerical answers should be correct at least up to three decimal places for full credit.

8. If you feel any question needs additional assumptions, you may indicate your assumptions in the

answer script and solve the problem accordingly. Please note that if we do not find the assumptions

necessary and/or reasonable, we may not award any marks.

9. Any suspected/proven case of cheating will be reported to the PGPX EC.

BEST OF LUCK!

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1. a) [2 Marks3 = 6 Marks] Indicate whether each of the following statements is TRUE or FALSE

with very brief reasoning. For this question you need to give reason for your answers to get credit.

i) If A, B and C are three events such that P(A|B) = P(A) and P(A|C) = P(A) where P(A) > 0, then A,

B and C are independent of each other.

ii) A store has two branches, say branch I and branch II. Customers arrive at branch I at the rate of 10

per minute and at branch II at the rate 5 per minute, both following Poisson processes. Then the

difference: number of people arriving at branch I-number of people arriving at branch II will follow a

Poisson process at the rate 5 per minute.

iii) If the marks distribution of 1000 students is approximately normal with mean M and variance

100, then the number of students scoring between M and M+15 is expected to be more than four

times the number of students scoring between M-15 and M-10.

b) [2 Marks] From a school, every year 150 students take the CBSE board examination after

finishing class X. 80% of them study in the same school for their plus two, half of them going for the

science stream and the rest for the commerce stream. In addition, the school admits 40 more

students, all to the commerce stream. Let us call the newly admitted students as outsiders, and the

students from the same school who join plus two as insiders.

The principal, a mathematics teacher, expects that on the average 60% of the top 10 students in

commerce would be the insiders.

i) What is the basis of the principals calculations?

ii) Are her calculations valid? Why or why not?

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2. Every year 200 students from a school take the IIT entrance examination. It is known that the

probability of cracking the IIT entrance examination for any student from that school is 0.01,

independently of the performance of any other student. Then,

a) [2 Marks] What is the probability that in 2016, at least 2 students from the school would crack the

IIT entrance examination?

b) [2 Marks] What is the distribution of the number of years, during the five year period 2016-2020,

when at least 2 students from the school crack the IIT entrance examination? Specify the distribution

completely.

c) [2 Marks] What is the probability that during the five year period 2016-2020, every year at least 2

students from the school would crack the IIT entrance examination?

d) [2 Marks] What is the probability that during the five year period 2016-2020, overall at least 10

students from the school would crack the IIT entrance examination?

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3. The FurnishHome Company is planning to buy a plot of land. The price of the land is Rs.200

crores now, in April. The price of the plot is likely to change from now till June. The following table

shows the three possible changes in the price of the plot from April to May.

Price change in May Probability

Increases by Rs.25 crores 0.2

Remains the same 0.6

Decreases by Rs.25 crores 0.2

Changes in the price of the plot from May to June depend on the price changes that take place in

May. The price in June can either remain the same as that in May or decrease by a further Rs.25

crores. As a result of these two price movements in May and June, in June the price of the plot will

remain the same as in April with a probability of 0.6, reduce by Rs.25 crores with a probability of0.16, and reduce by Rs.50 crores with a probability of 0.16. (Note that there is one more possibility.)

a) [2 Marks] If the price of the plot of land remains unchanged between April and May, with what

probability would the price of the land in June be less than the price in April?

b) [2 Marks] If the price of the plot of land increases by Rs.25 crores from April to May, with what

probability would the price of the land in June be more than the price in April?

c) [2 Marks] If the price of the plot of land decreases by Rs.25 crores from April to May, with what

probability would the price of the land in June be less than the price in May?

d) [2 Marks] Given that the price of the plot in June is less than the price in April, with what

probability would the price of the land in May be less than the price in April?

e) [2 Marks] Given that the price of the plot in June is less than the price in April, what would be the

expected price of the plot in May?

f) [2 Marks] What are the respective (unconditional) expected prices of the plot in May and in June?

Note: To simplify the problem, we ignore the possibility of any competitor buying the plot in

April/May.

END OF PAPER