The IIT Madras BS Statistics for Data Science I (Stats 1) End Term paper sat on 7 Aug 2022, in the May 2022 term: 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.
An urn contains 10 white balls and 3 black balls. Four balls are drawn from the urn without replacement. Let a random variable X be defined as the number of white balls drawn, what is the possible values 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
A fair coin is tossed three times. If X denote the number of heads followed immediately by a tail, then what is the expected value of X?
Correct answer
A student of B.Sc. Online Degree ran out of time while taking a quiz-exam and plans to guess on last 5 questions. Each question has 4 possible choices, one of which is correct. If the random variable X represents the number of questions answered correctly, among the last 5 questions, then find the Var(X). (Enter the answer correct to two decimal places)
Correct answer: 0.94 (accepted within ±0.03)
Which of the following options is/are incorrect for a variable having ratio scale of measurement?
Difference between the values of a variable can not be evaluated.
Order of the data is meaningful.
Multiplication and division of values of a variable is possible.
There is no absolute zero for a variable.
Correct answers
Difference between the values of a variable can not be evaluated.
There is no absolute zero for a variable.
Correct answer
What is the Interquartile range (IQR) of the dataset 42, 51, 62, 47, 38, 50, 54, 43?
4.5
42.5
52.5
10
Correct answer
10
An analyst did a survey to know about annual incomes of recent graduates of two different universities and the results are given in Table Q.1.
If a randomly selected graduate earns more than $40, 000, then what is the probability that he/she is from University B?
Correct answer
Six men and five women apply for a position of administrative in a company and two of the applicants are selected for the interview. If the random variables X and Y denote the number of male and number of female in the interview pool respectively, then calculate the value of E(X + Y ).
Correct answer: 2
Six letter words (with or without meaning) are made using the letters of the word ‘SACHIN’. If all the formed words are now arranged in ascending order, then find the serial number at which the word ‘SACHIN’ will appear.
Correct answer: 601
Probability mass function of a random variable X is given as
Based on the given information, answer the subquestions.
Find the value of k.
(Enter the answer correct to one decimal place)
Correct answer: 0.1
Probability mass function of a random variable X is given as
Based on the given information, answer the subquestions.
Correct answer
To participate in a game of prediction of runs scored by a team in a cricket match, one needs to pay an entry fee of 10 rupee. If the net gain is uniformly distributed between [-10,10] rupee. Then based on the given information answer the subquestions.
What is the probability that the absolute value of net gain for a person participating in the game will be less than 2 rupees?
Correct answer
To participate in a game of prediction of runs scored by a team in a cricket match, one needs to pay an entry fee of 10 rupee. If the net gain is uniformly distributed between [-10,10] rupee. Then based on the given information answer the subquestions.
What is the probability that a person participating in this game will have a net gain of 0 rupee?
Correct answer: 0
The ratio of boys to girls at IIT Madras is 1.5 : 1. If a group of 6 students is randomly selected, then based on the given information, answer the subquestions.
What is the probability that there will be at least one girl in the selected group of 6 students? (Enter the answer correct to two decimal places)
Correct answer: 0.95 (accepted within ±0.04)
The ratio of boys to girls at IIT Madras is 1.5 : 1. If a group of 6 students is randomly selected, then based on the given information, answer the subquestions.
What is the probability that there will be exactly 3 girls in the group given that there is at least one girl in the selected group of 6 students? (Enter the answer correct to two decimal places)
Correct answer: 0.29 (accepted within ±0.04)
