Contents
What is the definition of a probability mass function?
The process of assigning probabilities to specific values of a discrete random variable is what the probability mass function is and the following definition formalizes this. The probability mass function (pmf) (or frequency function) of a discrete random variable X assigns probabilities to the possible values of the random variable.
What is the mass function of two random variables?
Two or more discrete random variables have a joint probability mass function, which gives the probability of each possible combination of realizations for the random variables.
How to write the probability mass of X?
Let X be a discrete random variable of a function, then the probability mass function of a random variable X is given by It is noted that the probability function should fall on the condition : Here the Range (X) is a countable set and it can be written as { x 1, x 2, x 3, ….}.
How is a mass function different from a density function?
A probability mass function differs from a probability density function (PDF) in that the latter is associated with continuous rather than discrete random variables. A PDF must be integrated over an interval to yield a probability. The value of the random variable having the largest probability mass is called the mode.
Where does the probability function fall on the condition?
It is noted that the probability function should fall on the condition : Here the Range (X) is a countable set and it can be written as { x 1, x 2, x 3, ….}. This means that the random variable X takes the value x 1, x 2, x 3, …. These can also be stated as explained below.
Which is the cumulative distribution function of X?
The cumulative distribution function (CDF or cdf) of the random variable X has the following definition: The cdf is discussed in the text as well as in the notes but I wanted to point out a few things about this function. The cdf is not discussed in detail until section 2.4 but I feel that introducing it earlier is better.