Зміст курсу

Теорія ймовірностей

1. Ознайомемося з основними правилами

Випадкова змінна Схема Бернуллі 1/2 Схема Бернуллі 2/2 Біноміальна ймовірність 1/2 Біноміальна ймовірність 2/2

2. Ймовірності декількох подій

Додавання ймовірностей Обчислення зв'язаних ймовірностей Виклик Перемножуємо ймовірності Залежні ймовірності Закон повної ймовірності Теорема Байєса Виклик

3. Проводимо захоплюючі експерименти

Перший експеримент Другий експеримент Третій експеримент Поєднуйте свої знання

4. Дискретні розподіли

Дискретний рівномірний розподіл Обчислити захоплюючу ймовірність Розподіл Бернуллі Біноміальний розподіл Виклик Пуассонівський розподіл Виклик

5. Нормальний розподіл

Нормальний розподіл Виклик 1 Виклик 2

Другий експеримент

As we remember from the previous chapter, it was almost impossible to figure out the probability of getting exactly 1000 positive responses among 20 000 answers, with the probability of 20% of getting a positive answer. But let's simplify it a little bit by changing the first part of the task. Here, we should calculate the probability of getting 1000 or more positive answers.

General formula:

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

Example:

Explanation:

from scipy.stats import binom importing object from scipy.stats.
binom.sf(k = 1000, n = 20000, p=0.20) the probability of getting more than 1000(inclusive) successes amoung 20 000 trials with the probability of success 20 %

Interesting fact:

As we remember in the previous chapter, we received 0%, but here the probability is 1.0 or 100%. In this case, the enormous sample was for us; further, compare this output with the output in the task, where the sample is significantly less.

Завдання

Here, we should cope with almost the same task as in the previous chapter, but a little bit changed.

Your task here is to calculate the probability that 5 or more kittens will find a home, there are 12 kittens in the shelter. In this city, kittens are taken from a shelter with a probability of 75%. Import relevant library to do it.

The output here is going to be less hopeful.

The probability of that exactly 5 kittens will be taken is 0.011471271514892587.

Import binom object from scipy.stats.
Calculate the probability that '5' or more kittens of 12 will find home with the probability of success 75%.

The output here is going to be less hopeful.

Завдання

Here, we should cope with almost the same task as in the previous chapter, but a little bit changed.

The output here is going to be less hopeful.

The probability of that exactly 5 kittens will be taken is 0.011471271514892587.

Import binom object from scipy.stats.
Calculate the probability that '5' or more kittens of 12 will find home with the probability of success 75%.

The output here is going to be less hopeful.

Note
As we may recognize, in both cases the probability increased from the previous chapter to this one. By the way, our result will be less if we want to calculate a defined number of successes, try to allow our experiment to have an error.

Все було зрозуміло?

Секція 3. Розділ 2

Другий експеримент

General formula:

Example:

Explanation:

from scipy.stats import binom importing object from scipy.stats.
binom.sf(k = 1000, n = 20000, p=0.20) the probability of getting more than 1000(inclusive) successes amoung 20 000 trials with the probability of success 20 %

Interesting fact:

Завдання

Here, we should cope with almost the same task as in the previous chapter, but a little bit changed.

The output here is going to be less hopeful.

The probability of that exactly 5 kittens will be taken is 0.011471271514892587.

Import binom object from scipy.stats.
Calculate the probability that '5' or more kittens of 12 will find home with the probability of success 75%.

The output here is going to be less hopeful.

Завдання

Here, we should cope with almost the same task as in the previous chapter, but a little bit changed.

The output here is going to be less hopeful.

The probability of that exactly 5 kittens will be taken is 0.011471271514892587.

Import binom object from scipy.stats.
Calculate the probability that '5' or more kittens of 12 will find home with the probability of success 75%.

The output here is going to be less hopeful.

Note
As we may recognize, in both cases the probability increased from the previous chapter to this one. By the way, our result will be less if we want to calculate a defined number of successes, try to allow our experiment to have an error.

Все було зрозуміло?

Секція 3. Розділ 2

Другий експеримент

General formula:

Example:

Explanation:

from scipy.stats import binom importing object from scipy.stats.
binom.sf(k = 1000, n = 20000, p=0.20) the probability of getting more than 1000(inclusive) successes amoung 20 000 trials with the probability of success 20 %

Interesting fact:

Завдання

Here, we should cope with almost the same task as in the previous chapter, but a little bit changed.

The output here is going to be less hopeful.

The probability of that exactly 5 kittens will be taken is 0.011471271514892587.

Import binom object from scipy.stats.
Calculate the probability that '5' or more kittens of 12 will find home with the probability of success 75%.

The output here is going to be less hopeful.

Завдання

Here, we should cope with almost the same task as in the previous chapter, but a little bit changed.

The output here is going to be less hopeful.

The probability of that exactly 5 kittens will be taken is 0.011471271514892587.

Import binom object from scipy.stats.
Calculate the probability that '5' or more kittens of 12 will find home with the probability of success 75%.

The output here is going to be less hopeful.

Note
As we may recognize, in both cases the probability increased from the previous chapter to this one. By the way, our result will be less if we want to calculate a defined number of successes, try to allow our experiment to have an error.

Все було зрозуміло?

General formula:

Example:

Explanation:

from scipy.stats import binom importing object from scipy.stats.
binom.sf(k = 1000, n = 20000, p=0.20) the probability of getting more than 1000(inclusive) successes amoung 20 000 trials with the probability of success 20 %

Interesting fact:

Завдання

Here, we should cope with almost the same task as in the previous chapter, but a little bit changed.

The output here is going to be less hopeful.

The probability of that exactly 5 kittens will be taken is 0.011471271514892587.

Import binom object from scipy.stats.
Calculate the probability that '5' or more kittens of 12 will find home with the probability of success 75%.

The output here is going to be less hopeful.

Note
As we may recognize, in both cases the probability increased from the previous chapter to this one. By the way, our result will be less if we want to calculate a defined number of successes, try to allow our experiment to have an error.

Секція 3. Розділ 2

Перейдіть на комп'ютер для реальної практикиПродовжуйте з того місця, де ви зупинились, використовуючи один з наведених нижче варіантів