The IIT Madras BS Statistics for Data Science I (Stats 1) End Term paper sat on 24 Dec 2023, in the September 2023 term, set ADD3: 15 questions for 40 marks in 180 minutes. Every question is below with its answer. Take it as a timed mock test to be marked, or read it through first.
A repairman services five washing machines each day. For each machine, there is a 50% chance that the repair will involve installing a specific part. Find the probability that at most one washing machine out of the five will need this part for installation.
Correct answer
A shopkeeper has five red, four black and two blue pens. A customer went to his shop and selects three pens at random. Find the total number of ways in which the customer can select the pens of different colours.
20
11
40
65
Correct answer
40
A box contains 10 red balls and 3 blue balls. Four balls are drawn at random from the urn without replacement. Let the random variable X denote the number of red balls that are drawn from the box. Find the possible values that X can take.
{1, 2, 3, 4}
{1, 2, . . . , 10}
{0, 1, 2, 3, 4}
{0, 1, 2, . . . , 10}
Correct answer
{1, 2, 3, 4}
If X and Y are independent Poisson random variables with parameter 2, then find the Var(2X − Y) .
2
11
6
10
Correct answer
10
Which of the following statement(s) is/are true?
Vehicle Number plate has a nominal scale of measurement.
Phone brand has an ordinal scale of measurement.
Amount of milk (in litres) is a numeric and discrete variable.
Life of a bulb (in hours) has a ratio scale of measurement.
Correct answers
Vehicle Number plate has a nominal scale of measurement.
Life of a bulb (in hours) has a ratio scale of measurement.
Correct answer: 3
Correct answer: 0.156 (accepted within ±0.005)
How many numbers can be formed using the digits 0, 1, 3, 5, 7, 9 (without repetition), such that the number formed is greater than 20, 000?
Correct answer: 1080
From an ordinary deck of 52 cards, suppose five cards are selected at random without replacement. Find the probability that at least one card is a face card. Enter the answer correct to two decimal places.
Correct answer: 0.75 (accepted within ±0.03)
Suppose the lifetime of a radio is uniformly distributed between a to 150 weeks. Based on the given information, answer the sub questions:
If the expected lifetime of a radio is 130 weeks, then find the value of a.
Correct answer: 110
Suppose the lifetime of a radio is uniformly distributed between a to 150 weeks. Based on the given information, answer the sub questions:
What is the conditional probability that the battery will last for more than 140 weeks given that it has already worked for more than 130 weeks?
Correct answer
A telecom company is assessing the potential issues with its latest smartphone model. There is a probability of 0.35 for a software glitch, probability of 0.25 for battery issues, and 0.40 for defects in some other component.
Based on the above data, answer the given subquestions.
What is the probability that the issue is the software glitch or the battery, if the probability of having both issues simultaneously is 0.12?
0.48
0.60
0.09
0.20
Correct answer
0.48
A telecom company is assessing the potential issues with its latest smartphone model. There is a probability of 0.35 for a software glitch, probability of 0.25 for battery issues, and 0.40 for defects in some other component.
Based on the above data, answer the given subquestions.
What is the probability that there is no issue with either the software or the battery in the smartphone? Enter the answer correct to two decimal places.
Correct answer: 0.52 (accepted within ±0.02)
Based on the above data, answer the given subquestions.
Correct answer: 0.17 (accepted within ±0.03)
Based on the above data, answer the given subquestions.
0
1
0.5
0.33
Correct answer
1
