Description

Knowledge Discovery and Data Mining (CS 513)
(Midterm)

Prof. Khasha Dehnad

Student Name : Paras Garg
Course Section : CS 513-A
CWID : 10414982
Question 1 – For the experiment consisting of a single die toss, let A = {outcome is <= 3}, B = {1, 2, 5, 6} and C = {outcome is odd}. Please answer each of the following three True / False question. Show your work.
1.
2.
3.
Solution 1 – Since given,
A = {1, 2, 3}
B = {1, 2, 5, 6}
C = {1, 3, 5}

1.

2.

3.
Question 2 – Is the following function a proper distance function? Why? Explain your answer.

Hint: Measure the distance between
Solution 2 – Any distance function can only be a proper distance function if it follows the following properties:-
1.
2.
3.

Now, let us consider the three points in a coordinate system as

Case 1: Calculating distance between using above function

Case 2: Calculating distance between using above function

Case 3: Calculating distance between

Case 4: Calculating distance between using above function

Case 5: Calculating distance between using above function

Case 6: Calculating distance between

Checking the validity of the distance function properties on the distance values calculated by the given function.
Property 1:

For all cases property 1 satisfied
Property 2:
from case 1 and case 3
from case 4 and case 6
from case 2 and case 5

For all cases property 2 satisfied
Property 3:

From case 1, case 2 and case 4 From case 3, case 5 and case 6

,
Condition failed.
For both cases property 3 failed

As per the above calculations and observations, the cases satisfies the property 1 and the property 2 of distance function but do not satisfy the property 3. Therefore, the given function is not a proper distance function.

Question 4 – A telecommunications company is concerned about the number of customers leaving their business (Churn = True). Using past data, an analyst has prepared the table below. Using the table below, calculate the following probabilities.

International Voice
Plan Plan Churn
FALSE Churn
TRUE Row Total
no no 1,878 302 2,180
no yes 786 44 830
Sub-Total 2,664 346 3,010
yes no 130 101 231
yes yes 56 36 92
Sub-Total 186 137 323
GrandTotal 2,850 483 3,333

1.

2.

3.

4.

5.

6. Are “Voice Plan” and “International Plan” independent?
According to independent probability =>

,
%
The values on left side and right side is not equal implies condition for independent probability failed, so we can consider it as the “voice plan” and “international plan” are not independent or are dependent.
7.

8.

9.