1. ## Probability Distribution Function

Hello everyone, Ive encountered a problem during revision with the following question:

A money Box contains 80x10p and 120x20p coins. Two coins are taken out at random without replacement. Calculate the Probability Density Function (P.D.F), f(x), where x is the total monetary value of the coins taken out.

I originally tackled the problem by writing down all the possible outcomes:

10p + 10p = 20p
10p + 20p = 30p
20p + 10p = 30p
20p + 20p = 40p

As I currently understand it, the P.D.F should be the number of times an outcome occurs, divided by the total number of outcomes. So I worked out the P.D.F as:
f(20p) = 1/4,
f(30p) = 2/4,
f(40p) = 1/4.

However, according to the answers this is wrong. Can someone please explain where Ive gone wrong?

According to the answer booklet, the P.D.F should be:
f(20) = 0.1588
f(30) = 0.4824
f(40) = 0.3588

Any Help would be very much appreciated!

Alex

2. As I currently understand it, the P.D.F should be the number of times an outcome occurs, divided by the total number of outcomes.
This is where you are going wrong. the P.D.F is just the probability that the event occurs. Your list approach doesn't work because the different items in the list have different probabilities attached to them.

Lets take f(30) as an example

f(30)=p(10p and 20p) + p(20p and 10p)
=(80/200)*(120/199) + (120/200 * 80/199)
=0.4824

Can you do the rest from here?

3. Thank you very much! I can get the rest now!

I think the problem was the example from my notes I was using, it doesnt explain what the P.D.F is very well, but now I understand.

Thanks again!

Alex