BACHELOR OF COMPUTER SCIENCE (HONS)

BACHELOR OF INFORMATION TECHNOLOGY (HONS)

MAT 2204: MATHEMATICS FOR COMPUTING

ASSIGNMENT 3: AUGUST 2014 SESSION

Answer ALL Questions.

1. Find a solution to the recurrence relation

for n 3 with initial conditions and . (8 marks)

2. Solve the recurrence relation an = 14an-1 – 49an-2 for n 2 if a0 = 3 and a1 = 35. (7 marks)

3. A company owns a fleet of 950 cars, each having either manual or automatic transmission and either 2 or 4 doors. The following table shows the classification of 950 cars model. Model

2-door

4-door

Automatic

135

351

Manual

251

213

If a car is picked at random from the fleet, calculate the probability that it is:

(i) automatic, (2 marks) (ii) automatic or 2-door, (2 marks) (iii) manual and 4-door, (2 marks) (iv) 2-door given that it is manual transmission. (2 marks)

4. Consider a random variable M with the probabilities specified in the following figure: k 3

6

9

12

15

P (M = k)

(i) Find E (M). (2 marks) (ii) Find E (M2). (2 marks) (iii) Find the variance of the random variable M. (2 marks) (iv) Find the standard deviation of the random variable M. (2 marks)

5. 1200 employees were surveyed about their meals preference in the cafeteria. The following information was obtained:

Breakfast

Lunch

Dinner

Vegetarian Meal

184

237

182

Non Vegetarian Meal

206

200

191

(i) What is the probability that a randomly chosen employee prefers vegetarian meal and took lunch? (2 marks)

(ii) What is the probability that a randomly chosen employee took dinner or prefers non vegetarian meal? (2 marks)

(iii) What is the probability that a randomly chosen employee took breakfast given that he or she prefers vegetarian meal? (2 marks)

6. 600 employees were surveyed about their beverage preference in the cafeteria. The