Information Measures (graded) :Mastering Data Analysis in Excel (Excel to MySQL: Analytic Techniques for Business Specialization) Answers 2025

1. Question 1
   Which coin has larger entropy prior to observing outcome?

✔️ The fair coin
❌ The unfair coin

2. Question 2
   Entropy of one fair 6-sided die (before observing):

✔️ 2.58 bits
❌ 2.32 bits
❌ 0.46 bits
❌ 0.43 bits

3. Question 3
   Numbers 1001–5000 → max number of questions needed (binary strategy):

✔️ 12
❌ 11
❌ 13
❌ 10

4. Question 4
   Conditional Entropy H(X|Y) for a = 0.4, c = 0.5, e = 0.11:

✔️ 0.87 bits
❌ 1.87 bits
❌ 0.97 bits
❌ 0.90 bits

5. Question 5
   Given a = 0.3, c = 0.2 and H(X,Y) = H(X)+H(Y) → joint probability e =

✔️ 0.06
❌ 0.3
❌ 0.04
❌ 0.5

6. Question 6
   Given a = 0.2, c = 0.5 and true positive rate = 0.18 → Mutual Information:

✔️ 0.13 bits
❌ 0.08 bits
❌ 0.72 bits
❌ 1.64 bits

7. Question 7
   Monty Hall with 5 doors; you chose #1; Monty opens #2 and #3. Probability prize is behind door #4:

✔️ 0.4
❌ 0.5
❌ 0.67
❌ 0.2

8. Question 8
   Bits of information communicated by Monty (which two doors he opens) in 5-door Monty Hall:

✔️ 0.80 bits
❌ 1.52 bits
❌ 2.32 bits
❌ 0.67 bits

9. Question 9
   Prior: P(fair)=0.3, P(crooked)=0.7. p(head|fair)=0.5, p(head|crooked)=0.4. Observed heads → P(coin is fair) =

✔️ 0.35
❌ 0.15
❌ 0.40
❌ 0.43

10. Question 10
    Prior equal for fair/unfair die. P(3|fair)=1/6, P(3|unfair)=1/3. Observed 3 → P(die is fair) =

✔️ 0.33
❌ 0.08
❌ 0.23
❌ 0.36

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