# 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.

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