Question 1 (40 marks)

Consider the following item set: {Shampoo, Toothpaste, Detergent, Dish Soap, Oats, Tea, Wheat, Onions}

These items were purchased in various combinations during shopping online. The combination of buys is shown in the transactional record below:

Transaction 1: Shampoo, Toothpaste, Detergent, Transaction 2: Toothpaste, Detergent, Dish Soap, Transaction 3: Detergent, Dish Soap, Oats, tea, Transaction 4: Shampoo, Detergent, Dish Soap, tea, Wheat, Onions, Transaction 5: Dish Soap, tea, Wheat, Onions,

Create three association rules and calculate the confidence and support measures for each association rule.

Highlight the strongest association rule using the lift indicator.

(30 marks) (10 marks)

Question 2 (30 marks)

Suppose X N (10, 4) (a) Find:

(i) P(X > 13.4) (ii) P(8 < X < 9) (b) Find the value a such that P(10 - a < X < 10 + a) = 0.95 (c) Find the value b such that P(10 - b < X < 10 + b) = 0.99

(5 marks)

(5 marks) (10 marks) (10 marks)

Question 3 (30 marks)

If a person rolls a fair die twice and records the total score. The sample space will be: S = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

Let the following events be: A = total score is an even number B = total score is strictly less than 8 C = total score greater than 4, but less than 10

(a) Calculate the probability of event A. (b) Calculate the probability of event B. (c) Calculate the probability of event C.

(10 marks) (10 marks) (10 marks)

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