ANSWER ALL QUESTIONS (20 MARKS)

QUESTION ONE

A random variable X takes the integer value r with probability P(x) defined by:

Kx2

for x = 1, 2, 3

P(X=x) = K (7-x)

2

for x = 4, 5, 6

0 otherwise

i. Shows that =

1

28

(1 mark)

ii. Find the value of E(X)

(2 marks)

iii. Calculate the value for Var(3-4X)

(5 marks)

QUESTION TWO

A tetrahedral die is thrown and the number of the face on which it lands is noted. The probability

distribution shows in table below:

x 1 2 3 4

P(x) 0.25 a 0.25 0.25

i. Find the value of a

(1 mark)

ii. Shows that E(X) = 2.5

(2 marks)

iii. Shows that E(2X) = 2E(X)

(3 marks)

QUESTION THREE

The number of telephone calls made to the school office during a 5 minutes interval follows a

Poisson distribution with mean 0.5.Find the probability that :

i. No calls will be received between 10.05 and 10.15

(3 marks)

ii. More than 3 calls will be received during a particular period of 30 minutes

(3 marks)