# Thread: Probability Homework - Is it correct?? HELP!

1. ## Probability Homework - Is it correct?? HELP!

How can I do the second one?

Can someone be extremely helpful ?
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

(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.

(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.

2. Is it correct??

i) Mean(x) = P/Q = 1.5
where q = 1- p so using the P.G.F for a Geometric Distribution we have

P/1-P = 1.5
2.5.P = 1.5
Result P= 0.6 and Q=0.4

Probability Generating Function would be = q/ 1-ps

p.g.f(x)= 0.4 / 1 - 0.6s

Is it correct?? Do I need to do anything else?

thanks

3. 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.
You should go back and have another think. Post your progress after you've done this.

4. Originally Posted by wallace
How can I do the second one?

Can someone be extremely helpful ?
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

(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.

(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.