6.3: Probability Distributions
The probability of a random variable x is the likelihood of its occurrence. A probability distribution represents the probabilities of a random variable using a formula, graph, or table. There are two types of probability distribution– discrete probability distribution and continuous probability distribution.
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson probability distribution.
The binomial distribution is a probability distribution of a procedure with a fixed number of trials, where each trial has only two possible outcomes. A distribution involving coin tossing is an example of this distribution, as a coin toss has only two possible outcomes– heads or tails.
Poisson distribution is a distribution of independent events occurring over a specific interval. The number of messages received per day is an example of this type of distribution. A Poisson probability distribution of a discrete random variable gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. The Poisson distribution may be used to approximate the binomial if the probability of success is "small" (less than or equal to 0.05) and the number of trials is "large" (greater than or equal to 20).
Continuous probability distributions are the distributions associated with continuous random variables. They are divided into two categories– uniform distribution and normal distribution,
A uniform distribution is rectangular-shaped, indicating that the values are evenly spread over the range of possibilities. An example would be a distribution of hearts, spades, clubs, and diamonds in a deck of cards. This is because there is an equal probability of drawing a heart, a spade, a club, or a diamond from the card deck.
In contrast, a normal distribution is a probability distribution that forms a symmetric bell-shaped curve. Most IQ scores are normally distributed. Often real-estate prices fit a normal distribution. The normal distribution is extremely important, but it can only be applied to some things in the real world.
This text is adapted from Openstax, Introductory Statistics, Section 4.