We know that a random variable is an uncertain quantity or a number. Its value is determined by chance. For example, the outcome of rolling a die is random. We could get any number from 1 to 6. In case of a die, the probability of getting any number is 1/6. Each outcome has the same probability. However, the probability of each outcome could be different.
A probability distribution is a graph or a table that describes the probabilities of each outcome of a random variable.
In a probability distribution, each value or outcome of the random variable is represented as x. The probability of getting x is represented as P(x). So, if X is the random variable, we are saying that the probability of random variable X being equal to x is P(X=x) or P(x). This is called the probability function.
The probability distribution of rolling a die is shown below:
| xi | P(xi) |
| 1 | 1/6 |
| 2 | 1/6 |
| 3 | 1/6 |
| 4 | 1/6 |
| 5 | 1/6 |
| 6 | 1/6 |
Note that the sum of all probabilities should be equal to 1 and the probability of each outcome, P(x) is between 0 and 1.