Originally Posted by

**wallace** [snip]

Question 3 (Unit 1)

– 10 marks

(a)

The random variables V

and W

have the following probability generating

functions.

(i)

ΠV (s)= 7s / 10 - 3s

(ii)

ΠW (s)= (7 + 3s / 10 ) power of 8

Use the table of discrete probability distributions on page 4 of the Handbook

to identify the distribution of each of the random variables. In each case, you

should name a family of distributions and give the values of any parameters.

p(X=x)

I haven't got a clue how to do it

Mr F says: Have you looked at page 4? Which ones have the same form as what you've been given ....?

(b)

The number of items bought by each customer entering a chemist’s shop is a

random variable Xthat has a geometric distribution starting at 0 with mean

1.5.

(i)

Find the value of the parameter pof the geometric distribution and

hence write down the probability generating function of X.

Mr F says: It should be obvious that you would solve (1 - p)/p = 1.5 .... Now substitute p into the relevant pgf.

(ii)

Six customers visit the shop. The number of items bought by a

customer is independent of the number bought by any other customer.

Write down the probability generating function of Y, the total number

of items they buy. Use the table of discrete probability distributions on

page 4 of the Handbook to identify the distribution of Y, and hence find

the mean and variance of the total number of items purchased by the six

customers.