Probability distribution and discrete probability distribution

Probability Distribution - We have explored the idea of probability we can consider the concept of a probability distribution. In situations where the variable being studied is a random variable, then this can often be modeled by the probability distribution. Simply put, a probability distribution has two components - the collection of possible values that the variable can take, together with the probability that each of these values (or a subset of these values) occurs.

So, in stochastic modeling, a probability distribution is the equivalent of a function in deterministic modeling (in which there is no uncertainty). As we know, there are many different functions available for deterministic modeling and some of these are used more often than others e.g., linear functions, polynomial functions, and exponential functions. Exactly the same situation prevails in stochastic modeling. Certain probability distributions are used more often than others. These include the Binomial distribution, the Poisson distribution, the uniform distribution, the normal distribution, and the negative exponential distribution.

Discrete Probability Distributions - A discrete random variable assumes each of its values with a certain probability, i.e. each possible value of the random variable has an associated probability. Let X be a discrete random variable and let each value of the random variable have an associated probability, denoted p(x) = =p(X = x),such that

p(x) is also referred to as the probability function or probability mass function.