# Probability theory: Random variable, Distribution of the discrete random variable

This is part of the course “Probability Theory and Statistics for Programmers”.

**Random variable **— is a variable whose possible values are outcomes of a random experiment. For example the number of hits during the three shots(*0, 1, 2, 3)*, or sum of the upward face after rolling 5 dice(5 … 25). This is examples of **discrete random variables, **variables with a fixed amount of possible values. Another type is **continuous random variable** — the variable that can take any value on the interval. For example, speed or mass of some random object.

Let’s take a closer look at discrete random variables. The discrete random variable has a number of possible values, each value has it is own probability. Since events are a mutually exclusive sum of all their probabilities equal to one.

A random variable will be completely described if we specify distribution — probability for each event. This way we can specify the Law of distribution of the discrete variable.

**The law of distribution of a random variable** is any relation that establishes a connection between the possible values of a random variable and the corresponding probabilities.

Example. Some shooter fires on the target until the first hit and he has 4 shells. Probability of hit is 0.6. We should find the distribution of unused shells.

Reach the next level of focus and productivity with increaser.org.