Course Content

Probability Theory

1. Learn Basic Rules

Random Variable Bernoulli Trial 1/2 Bernoulli Trial 2/2 Binomial Probability 1/2 Binomial probability 2/2

2. Probabilities of Several Events

Add Probabilities Calculate Connected Probabilities Challenge Multiply probabilities Dependent probabilities Law of Total Probability Bayes Theorem Challenge

3. Conducting Fascinating Experiments

The First Experiment The Second Experiment The Third Experiment Combine Your Knowledge

4. Discrete Distributions

Discrete Uniform Distribution Calculate Fascinating Probability Bernoulli Distribution Binomial Distribution Challenge Poisson Distribution Challenge

5. Normal Distribution

Normal Distribution Challenge 1 Сhallenge 2

The Third Experiment

It is time to move to the third experiment, which should be useful for we as for data scientist!

General formula:

In this experiment, we will work with the binom.cdf(k, n, p) function. This function helps calculate the probability of receiving k or less successes among n trials with the probability of success for each experiment p.

Real-life example:

Imagine that we are working for the bank, and last month the bank gained 200 customers; we know that the probability for clients to continue working with the bank is 60%. Calculate the probability that 70 or fewer customers will stay with we.

Code:

Explanation:

from scipy.stats import binom importing object from scipy.stats.
binom.cdf(k = 70, n = 200, p=0.60) the probability of getting 70 or less successes amoung 200 trials with the probability of success 60 %

By the way, this function is one of the most commonly used. Indeed it is hard to get zero here because we need 70 or less(in this case), so 1 is a relevant result too! In comparison to the previous functions(experiments) where we would receive at least or exactly defined number of successes.

Task

Imagine that we work with real research.

Our task here is to calculate the probability that 10 or fewer residents in a specific town with a population of 500 will answer yes to our question, "Do you have your housing?". The probability that the answer will be positive is 40%.

Import binom object from scipy.stats.
Calculate the probability that 10 or fewer people among 500 interviewees will answer "yes", the probability of receiving positive answer is 40%.

Task

Imagine that we work with real research.

Import binom object from scipy.stats.
Calculate the probability that 10 or fewer people among 500 interviewees will answer "yes", the probability of receiving positive answer is 40%.

Everything was clear?

Section 3. Chapter 3

The Third Experiment

It is time to move to the third experiment, which should be useful for we as for data scientist!

General formula:

Real-life example:

Code:

Explanation:

from scipy.stats import binom importing object from scipy.stats.
binom.cdf(k = 70, n = 200, p=0.60) the probability of getting 70 or less successes amoung 200 trials with the probability of success 60 %

Task

Imagine that we work with real research.

Import binom object from scipy.stats.
Calculate the probability that 10 or fewer people among 500 interviewees will answer "yes", the probability of receiving positive answer is 40%.

Task

Imagine that we work with real research.

Import binom object from scipy.stats.
Calculate the probability that 10 or fewer people among 500 interviewees will answer "yes", the probability of receiving positive answer is 40%.

Everything was clear?

Section 3. Chapter 3

The Third Experiment

It is time to move to the third experiment, which should be useful for we as for data scientist!

General formula:

Real-life example:

Code:

Explanation:

from scipy.stats import binom importing object from scipy.stats.
binom.cdf(k = 70, n = 200, p=0.60) the probability of getting 70 or less successes amoung 200 trials with the probability of success 60 %

Task

Imagine that we work with real research.

Import binom object from scipy.stats.
Calculate the probability that 10 or fewer people among 500 interviewees will answer "yes", the probability of receiving positive answer is 40%.

Task

Imagine that we work with real research.

Import binom object from scipy.stats.
Calculate the probability that 10 or fewer people among 500 interviewees will answer "yes", the probability of receiving positive answer is 40%.

Everything was clear?

It is time to move to the third experiment, which should be useful for we as for data scientist!

General formula:

Real-life example:

Code:

Explanation:

from scipy.stats import binom importing object from scipy.stats.
binom.cdf(k = 70, n = 200, p=0.60) the probability of getting 70 or less successes amoung 200 trials with the probability of success 60 %

Task

Imagine that we work with real research.

Import binom object from scipy.stats.
Calculate the probability that 10 or fewer people among 500 interviewees will answer "yes", the probability of receiving positive answer is 40%.

Section 3. Chapter 3

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