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!