Assignment 3

INTI INTERNATIONAL UNIVERSITY

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