Homework Help: Probability Mass Function of a Discrete Non-Uniform Distribution

1. Oct 23, 2012

iTee

1. The problem statement, all variables and given/known data

I'm having trouble understanding PMF. We are given a number, say, 927189234.

We need to calculate the PMF of (0, 1, ..., 9) in this distribution.

2. Relevant equations

3. The attempt at a solution

Calculating the probabilities is easy,

P(9) = 2/9
P(8) = 1/9
.
.
.
P(0) = 0/9

I fail to understand if this is the same as the PMF.

Any help would be greatly appreciated.

2. Oct 23, 2012

Ray Vickson

What do YOU think is meant by the term PMF?

RGV

3. Oct 23, 2012

iTee

-None-

Last edited: Oct 23, 2012
4. Oct 23, 2012

iTee

I've understood the PMF by graphing it out,

So if the X-axis is the (0,1 ..., 9) and the Y-axis are the probabilities, the height of each X-axis value is its PMF. But I don't understand how the Y-axis probabilities are calculated or would they be 0, 1/9, 2/9..., 1.

I've read that the PMF >= 0 and that the sum of the PMF's of all possible values in a distribution should be equal to 1.

5. Oct 23, 2012

Ray Vickson

Exactly!---although very badly worded. (You don't sum the PMFs; there is just one single PMF and it is a table of the probability values; you are not summing different tables, you are just summing the things in a single table.) So the values of the PMF cannot be 0, 1/9, 2/9, ..., 1 because when you sum these you get something much larger than 1. You seem to be confusing PMF and CDF.

RGV

6. Oct 23, 2012

iTee

PMF of 9 is 2/9.

Last edited: Oct 23, 2012
7. Oct 23, 2012

Ray Vickson

Yes.

RGV

8. Oct 23, 2012

iTee

So the table of PMF is
{2/9, 2/9, 1/9, 1/9, 1/9, 1/9, 1/9}
?

Thank you.

9. Oct 23, 2012

Ray Vickson

Not quite; you also need to specify the x values (and you need to include zero). I liked your original description P(0) = 0, P(1) = 2/9, etc. much better. That says it all. Or you could make a table with x values in one column (or row) and P(x) values in the other column (or row).

RGV