Probability distribution function

In probability theory, a probability distribution is a statistical function that describes all the possible values and likelihoods that a random variable can take within a given range. Generally, we denote the random variable by X, and the likelihood that this random variable takes a specific value of X is denoted by p(X).

The probability of any event A is calculated by this formula:

Now, let us take an example of a coin toss. 

A coin toss always leads to one outcome or value.

If we denote that outcome as X here, then the probability distribution of X would take the value 0.5 (1 in 2 or 1/2) for X = heads, and 0.5 for X = tails.

Examples of random phenomena include the weather conditions at some future date, the height of a randomly selected person, etc.