Question

4. Bayes Theorem - One way of thinking about Bayes theorem is that it converts a-priori probability to a-posteriori probability meaning that the probability of an event gets changed based upon actual observation or upon experimental data. Suppose you know that there are two plants that produce helicopter doors: Plant 1 produces 1000 helicopter doors per day and Plant 2 produces 4000 helicopter doors per day. The overall percentage of defective helicopter doors is 0.01%, and of all defective helicopter doors, it is observed that 50% come from Plant 1 and 50% come from Plant 2. [8 points]

(i) The a-posteriori probability of defective helicopter doors produced by Plant 1 is:

a. 0.0025

b. 0.025%

c. 0.25%

d. 0.015%

Clustering [4 Points]   

(ii)K-Means clustering algorithm

a. Needs K-means++ to know the optimal location of the centroids

b. Needs K-means++ to know the optimal number of clusters

c. Is a supervised algorithm

d. Provides the optimal clustering of points even if the initialization is bad

Answer 1

4) Option (b) is the correct answer.

Helicopter doors produced by Plant 1 = 1000 units

Helicopter doors produced by Plant 2 = 4000 units

Overall defective helicopter doors percentage = 0.01% = ((4000 + 1000) * 0.01) = 50 units

Defective percentage by plant 1 from overall = 50% of 50 = 25 units

Defective percentage by plant 2 from overall = 50% of 50 = 25 units

The a-posteriori probability of defective helicopter doors produced by Plant 1 = (number of defective doors / total number of doors) = 25 / 1000 = 0.025

Option (a) is incorrect as the probability given is wrong (correct is 0.025).

Option (c) is incorrect as the probability given is wrong (correct is 0.025).

Option (d) is incorrect as the probability given is wrong (correct is 0.025).

Second Question:

Option (a) is the correct answer.

K-Means clustering algorithm needs K-means++ to know the optimal location of the centroids.

Option (b) is incorrect as K-Means clustering algorithm does not need K-means++ to know the optimal number of clusters.

Option (c) is incorrect as K-Means clustering algorithm is an unsupervised algorithm.

Option (d) is incorrect as K-Means clustering algorithm provides the bad clustering of points if the initialization is bad.

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