Probability Mass Function of a Discrete Non-Uniform Distribution

[iTee]

Homework Statement

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.

Homework Equations

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.

 

[Ray Vickson]

Homework Statement

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.

Homework Equations

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.

What do YOU think is meant by the term PMF?

RGV

 

[iTee]

-None-

 

[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.

 

[Ray Vickson]

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.

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

 

[iTee]

PMF of 9 is 2/9.

 

[Ray Vickson]

Yes.

RGV

 

[iTee]

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

Thank you.

 

[Ray Vickson]

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

Thank you.

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