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A random variable that can take on an infinite number of possible values is known as a continuous random variable. Such a variable is defined over an interval of values rather than a specific value. An example of a continuous random variable is the weight of a person. In general, quantities such as pressure, height, mass, weight, density, volume, temperature, and distance are examples of continuous random variables. The probability that a continuous random variable takes on an exact value is 0 thus, a probability density function is used to describe such a variable.

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Discrete random variables are random variables, whose range is a countable set. A countable set can be either a finite set or a countably infinite set. A probability distribution is used to determine what values a random variable can take and how often does it take on these values. For instance, in the above example, X is a discrete variable as its range is a finite set ({0, 1, 2}). Another examples of discrete random variables include the number of children in a family, the Friday night attendance at a cinema, the number of patients in a doctor's surgery, the number of defective light bulbs in a box of ten.

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Associated with Discrete Random Variables

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A random variable that represents the number of successes in a binomial experiment is known as a binomial random variable. A binomial experiment has a fixed number of repeated Bernoulli trials and can only have two outcomes, i.e., success or failure. The number of trials is given by n and the success probability is represented by p.

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Associated with Discrete Random Variables

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A geometric random variable is a random variable that denotes the number of consecutive failures in a Bernoulli trial until the first success is obtained. The probability of success in a Bernoulli trial is given by p and the probability of failure is 1 - p.

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Associated with Discrete Random Variables

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A Bernoulli random variable is the simplest type of random variable. It can take only two possible values, i.e., 1 to represent a success and 0 to represent a failure.

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Associated with Discrete Random Variables

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A Poisson random variable is used to show how many times an event will occur within a given time period. These events occur independently and at a constant rate. The parameter of a Poisson distribution is given by λ which is always greater than 0.

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Associated with Continuous Random Variables

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An exponential random variable is used to model an exponential distribution which shows the time elapsed between two events. The parameter of an exponential distribution is given by λ.

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Associated with Continuous Random Variables

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A random variable that follows a normal distribution is known as a normal random variable. The parameters of a normal random variable are the mean μ and variance σ^2.