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NPTEL Introduction to Machine Learning Assignment Answers Week 4
Q1. A man is known to speak the truth 2 out of 3 times. He throws a die and reports that the number obtained is 4. Find the probability that the number obtained is actually 4:
a. 2/3
b. 3/4
c. 5/22
d. 2/7
Answer: d. 2/7
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Q2. Consider the following graphical model, mark which of the following pair of random variables are independent given no evidence?
A. a,b
B. c,d
C. e,d
D. c,e
Answer: A. a,b
Q3. Two cards are drawn at random from a deck of 52 cards without replacement. What is the probability of drawing a 2 and an Ace in that order?
a. 4/51
b. 1/13
c. 4/256
d. 4/663
Answer: d. 4/663
Q4. Consider the following Bayesian network. The random variables given in the model are modeled as discrete variables (Rain = R, Sprinkler = S and Wet Grass = W) and the corresponding probability values are given below.
P(R) = 0.1
P(S) = 0.2
P(WR, S) = 0.8
P(WIR,S)= 0.7
P(WR, S) = 0.6
P(WR,S) = 0.5
Calculate P(S| W, R).
a. 1.
b. 0.5.
c. 0.22.
d. 0.78
Answer: c. 0.22
Q5. What is the naive assumption in a Naive Bayes Classifier?
a. All the classes are independent of each other
b. All the features of a class are independent of each other
c. The most probable feature for a class is the most important feature to be considered for classification
d. All the features of a class are conditionally dependent on each other.
Answer: b. All the features of a class are independent of each other
Q6. A drug test (random variable T) has 1% false positives (ie., 1% of those not taking drugs show positive in the test), and 5% false negatives (i.e., 5% of those taking drugs test negative). Suppose that 2% of those tested are taking drugs. Determine the probability that somebody who tests positive is actually taking drugs (random variable D).
a. 0.66
b. 0.34
c. 0.50
d. 0.91
Answer: a. 0.66
Q7. It is given that P(A|B) = 2/3 and P(A|B) = 1/4. Compute the value of P(B|A).
a. 1/2
b. 2/3
c. 3/4
d. Not enough information.
Answer: d. Not enough information.
Q8. What is the joint probability distribution in terms of conditional probabilities?
a. P(D1) * P(D2|D1) * P(S1|D1) * P(S2|D1) * P(S3|D2)
b. P(D1) * P(D2) * P(S1|D1) * P(S2|D1) * P(S3|D1, D2)
c. P(D1) * P(D2) * P(S1|D2) * P(S2|D2) * P(S3|D2)
d. P(D1) * P(D2) * P(S1|D1) * P(S2|D1, D2) * P(S3|D2)
Answer: d. P(D1) * P(D2) * P(S1|D1) * P(S2|D1, D2) * P(S3|D2)
Q9. Suppose P(D1)=0.5. P(D2)=0.6. P(S1 D1)=0.4 and P(S1| D1′)=0.6. Find P(S1)
a. 0.14
b. 0.36
c. 0.50
d. 0.66
Answer : c. 0.50
Q10. In a Bayesian network a node with only outgoing edge(s) represents
a. a variable conditionally independent of the other variables.
b. a variable dependent on its siblings.
c. a variable whose dependency is uncertain.
d. None of the above.
Answer: a. a variable conditionally independent of the other variables.
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