The IIT Madras BS Statistics for Data Science II (Stats 2) Quiz 1 paper sat on 11 Jul 2021, in the May 2021 term, set POD21QZBQPA: 19 questions for 25 marks in 120 minutes. Every question is below with its answer. Take it as a timed mock test to be marked, or read it through first.
Use the following information to answer the given subquestions.
Consider 4 bits, where each bit can be either 0 or 1, transmitted over a noisy channel, i.e., there is a possibility of error. The probability of 1 bit getting changed is p, independent of all other bits. Let the random variable X denote the number of bits that changed.
Identify the distribution of X.
Correct answer
Use the following information to answer the given subquestions.
Consider 4 bits, where each bit can be either 0 or 1, transmitted over a noisy channel, i.e., there is a possibility of error. The probability of 1 bit getting changed is p, independent of all other bits. Let the random variable X denote the number of bits that changed.
Suppose the number of errors in 5 transmissions are x1 = 0, x2 = 1, x3 = 0, x4 = 2, x5 = 0: What is the likelihood function of p?
Correct answer
Use the following information to answer the given subquestions.
Consider 4 bits, where each bit can be either 0 or 1, transmitted over a noisy channel, i.e., there is a possibility of error. The probability of 1 bit getting changed is p, independent of all other bits. Let the random variable X denote the number of bits that changed.
Suppose the number of errors in 5 transmissions are x1 = 0, x2 = 1, x3 = 0, x4 = 2, x5 = 0: Find the Maximum likelihood estimate for p. Enter the answer correct to two decimal places.
Correct answer: 0.15
Based on the above data, answer the given subquestions.
Calculate the first moment of X.
Correct answer
Based on the above data, answer the given subquestions.
Correct answer: 1.8
Based on the above data, answer the given subquestions.
Correct answer: 0.4
Based on the above data, answer the given subquestions.
Find the likelihood function for the given sample.
Correct answer
Based on the above data, answer the given subquestions.
NOTE: Enter your answer to the nearest integer.
Correct answer: 3
Based on the above data, answer the given subquestions.
Are X and Y independent?
Yes
No
Correct answer
Yes
Based on the above data, answer the given subquestions.
Find the value of P(X > Y). Write your answer correct to two decimal places.
Correct answer: 0.55 (accepted within ±0.03)
Correct answer
A random sample of size 300 is collected from a population with a standard deviation of 20. Find a lower bound on the probability that the sample mean will be at most 4 away from the actual mean using the weak law of large numbers.
Correct answer
Use the following information to answer the given subquestions.
Correct answer: 1.33 (accepted within ±0.03)
Use the following information to answer the given subquestions.
Correct answer
Use the following information to answer the given subquestions.
Correct answer: 0.625 (accepted within ±0.025)
Correct answer
Correct answer
Based on the above data, answer the given subquestions.
Find the moment generating function of X.
Correct answer
Based on the above data, answer the given subquestions.
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