iTee said: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.
iTee said: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.
iTee said:So the table of PMF is
{2/9, 2/9, 1/9, 1/9, 1/9, 1/9, 1/9}
?
Thank you.
A probability mass function (PMF) is a function that maps each possible outcome of a discrete random variable to its probability of occurrence. It represents the probability distribution of a discrete random variable.
A discrete non-uniform distribution is a probability distribution where the outcomes are discrete (distinct and separate) and the probabilities associated with each outcome are not equal. This means that some outcomes are more likely to occur than others.
The PMF of a discrete non-uniform distribution can be calculated by dividing the number of times a specific outcome occurs by the total number of outcomes. This will give you the probability of that outcome occurring.
The main difference between a discrete non-uniform distribution and a discrete uniform distribution is that the probabilities associated with each outcome in a discrete non-uniform distribution are not equal, while in a discrete uniform distribution, all outcomes have equal probabilities. This means that in a discrete non-uniform distribution, some outcomes are more likely to occur than others, while in a discrete uniform distribution, all outcomes have an equal chance of occurring.
The PMF of a discrete non-uniform distribution can be interpreted as the likelihood of a specific outcome occurring. The higher the probability associated with an outcome, the more likely it is to occur. Additionally, the PMF can also provide information about the shape and spread of the distribution, such as the most likely outcome and the range of possible outcomes.