**Continuous distribution** describes the stochastic experiment with infinite possible outcomes.   
**Continuous uniform distribution** describes an experiment where all outcomes within the interval have an equal probability of occurring.   
If the variable is uniformly distributed, we can use a geometrical approach to calculate probabilities.    
Let's look at the example:   

Consider a line segment of length `10` units. What is the probability of randomly selecting a point on the line segment such that the distance from the starting point to this point is between `3 and 7` units?

As a result, position or the point is uniformly distributed on the line with length `10`. We can simply divide the length of the desired interval by the whole length of the segment.   
We can also use `.cdf()` method on `scipy.stats.uniform` class to calculate the corresponding probability:


from scipy.stats import uniform
# Parameters of an experiment
whole_length = 10
range_start = 4
range_end = 7

# Geometrical approach
desired_length = range_end - range_start
geom_proba = desired_length / whole_length
print(f'Geometrical probability is {geom_proba:.4f}')

# Using .cdf() method
upper_cdf = uniform.cdf(range_end, loc=0, scale=whole_length)
lower_cdf = uniform.cdf(range_start, loc=0, scale=whole_length)
cdf_proba = upper_cdf - lower_cdf
print(f'Probability using .cdf() is {cdf_proba:.4f}')

The first parameter of the `.cdf()` method determines the point at which we calculate probability; `loc` parameter determines the beginning of the segment, and `scale` determines the length of the segment.

The `.cdf()` method calculates the probability that an experiment's result falls into a certain interval: `.cdf(interval_end) - .cdf(interval_start)`.   
We will consider this method in more detail in [Advanced Techniques in Probability and Statistics](https://codefinity.com/courses/v2/ec6e4978-d3b4-4612-b2be-894504d0f970) course.

We will start our way of learning probability theory by considering some basic definitions and rules: what is a stochastic experiment and random event, what is independence and incompatibility of events in the context of probability theory, what is the probability and how can we calculate probabilities of different elementary events. 

In real-life tasks, we often have to deal with complex relationships and, as a result, calculate probabilities of several events or events that depend on each other. Let's consider how we can do this using probability theory.

To solve many real problems in probability theory, special models have been created that describe a particular situation. Let's consider some of the most used models that can be used to describe some discrete results of stochastic experiments.

What if the result of a stochastic experiment cannot be described by a discrete value? For this, models that work with continuous values are used. Consider the most popular of these models.

Often we are faced with the task of checking the dependence of the results of different stochastic experiments on each other. Moreover, it is necessary not only to assess the presence of dependencies but also to somehow quantify the degree of dependencies. To solve these problems, we can use covariance and correlation.

Probability Theory Basics

Continuous Uniform Distribution