Contenu du cours

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

Binomial Distribution

It is time to figure out what Binomial distribution is.

To work with this distribution, we should import the binom object from scipy.stats, and then you can apply numerous functions to this distribution like pmf, sf, and cdf that were already learned.

Key characteristics:

This distribution is the same as the Bernoulli distribution, which is repeated several times.

Example:

Tossing a coin is a Bernoulli distribution, but tossing one coin 3 times creates a binomial distribution.

binomial

By the way, Y-axis defines the probability in percents, for the better understanding(in this chapter and the next).

Do you remember the function .cdf()? The function shows the probability of having k or fewer successes among n trials with the defined probability p. It is time to recall it!

Tâche

Swipe to start coding

Imagine you passing a test that includes 12 questions; there are just two answers for each question (one of them is correct, another isn't correct). The probability of getting the right answer is 50% or 0.5. Here is the distribution:

binom

You have excellent marks, and you know that if you receive less than 6 or exactly 7 points, you will spoil it.

Import binom object.
Calculate the probability of receiving 6 or less points in the test where the probability of answering right is 0.5 and the number of questions is 12.
Calculate the probability of receiving exactly 7 points in the test where the probability of answering right is 0.5 and the number of questions is 12.
Calculate the whole probability.

Solution

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Tout était clair ?

Merci pour vos commentaires !

Section 4. Chapitre 4

Binomial Distribution

It is time to figure out what Binomial distribution is.

Key characteristics:

This distribution is the same as the Bernoulli distribution, which is repeated several times.

Example:

Tossing a coin is a Bernoulli distribution, but tossing one coin 3 times creates a binomial distribution.

binomial

By the way, Y-axis defines the probability in percents, for the better understanding(in this chapter and the next).

Do you remember the function .cdf()? The function shows the probability of having k or fewer successes among n trials with the defined probability p. It is time to recall it!

Tâche

Swipe to start coding

binom

You have excellent marks, and you know that if you receive less than 6 or exactly 7 points, you will spoil it.

Import binom object.
Calculate the probability of receiving 6 or less points in the test where the probability of answering right is 0.5 and the number of questions is 12.
Calculate the probability of receiving exactly 7 points in the test where the probability of answering right is 0.5 and the number of questions is 12.
Calculate the whole probability.

Solution

Passez à un bureau pour une pratique réelleContinuez d'où vous êtes en utilisant l'une des options ci-dessous

Tout était clair ?

Merci pour vos commentaires !

Section 4. Chapitre 4

Passez à un bureau pour une pratique réelleContinuez d'où vous êtes en utilisant l'une des options ci-dessous