A probability distribution specifies the probabilities of the possible outcomes of a random variable. There are primarily four probability distributions that are used extensively in investment analysis - uniform, binomial, normal, and lognormal probability distribution. The probability distribution function helps us in identifying the possibilities of return and risk inherent in investments.
A random variable is a quantity whose future outcomes are uncertain. A discrete random variable is a random variable that can take on a countable number of possible values. For example - the number of mutual funds beating the return of the market index. The number of funds can be easily countable. A continuous random variable can take an infinite number of possible values. For example - the time taken by a trader to execute a particular trade. The time taken can be 1 second, 1.01 second, 1.001 seconds, 1.0001 seconds and so on. It can take an infinite number of values that cannot be counted.
A probability function specifies the probability that a random variable takes on a particular value. P(X=x) is a probability that a random variable X takes on the value x. Here, the capital X represent the random variable, and the lower case x represent a specific value that the random variable can take.
For a discrete random variable, the notation for the probability function is p(x) = P(X=x). For a continuous random variable, the notation for the probability function is f(x), and it is also called as the probability density function (pdf).
Next LOS: Possible outcomes of a specified discrete random variable
