Binomial and Geometric Distribution 

A random variable is a variable that takes specific probilities. It can be thought of as a variable whose value depends on the outcome of an uncertain events.

The probabilities assigned to the possible values of a random variable are its distribution. A distribution completely describes a random variable.

A random variable is called discrete if it has countably many possible values; otherwise, it is called continues. 

Then the random variable is discrete. If the possible values are any of these:

• all numbers between 0 and ∞

• all numbers between -∞ and +∞

• all numbers between 0 and 1

The CDF of discrete random variables resembles a staircase, a graph with many jumps.

In the theory of probability and statistics, a Bernoulli trial is a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted.

Independent repeated trials of an experiment with exactly two possible outcomes are called Bernoulli trials. Call one of the outcomes "success" and the other outcome "failure". Let 𝑝 be the probability of success in a Bernoulli trial, and 𝑞 be the probability of failure. Then the probability of success and the probability of failure sum to one, since these are complementary events: "success" and "failure" are mutually exclusive and exhaustive. Thus, one has the following relations:

𝑝=1−𝑞, 𝑞=1−𝑝, 𝑝+𝑞=1.

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