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Теорія ймовірностей
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Зміст курсу

Теорія ймовірностей

Теорія ймовірностей

1. Ознайомемося з основними правилами
Випадкова зміннаСхема Бернуллі 1/2Схема Бернуллі 2/2Біноміальна ймовірність 1/2Біноміальна ймовірність 2/2
2. Ймовірності декількох подій
Додавання ймовірностейОбчислення зв'язаних ймовірностейВикликПеремножуємо ймовірностіЗалежні ймовірностіЗакон повної ймовірностіТеорема БайєсаВиклик
3. Проводимо захоплюючі експерименти
Перший експериментДругий експериментТретій експериментПоєднуйте свої знання
4. Дискретні розподіли
Дискретний рівномірний розподілОбчислити захоплюючу ймовірністьРозподіл БернулліБіноміальний розподілВикликПуассонівський розподілВиклик
5. Нормальний розподіл
Нормальний розподілВиклик 1Виклик 2

Обчислити захоплюючу ймовірність

Have you ever wonder that your friends birthday could be any day of the year with equal probability. The probability for each day creates uniform distribution.

Let's recall some functions, but for the uniform distribution (they are a little bit different): For calculating the probability of receiving exactly defined output x :

uniform.pdf(x, loc, scale).

For calculating the probability of receiving output that is bigger than x:

uniform.sf(x, loc, scale)(inclusive).

For calculating the probability of receiving output that is less than x:

uniform.cdf(x, loc, scale)(inclusive).

  • loc is the lower bound of the distribution (minimum value).
  • scale is the upper bound of the distribution (maximum value).

Завдання

Imagine that you met a person and want to calculate the probability of his birthday in summer, you know he wasn't born on a leap year. So, follow the algorithm:

  1. Import uniform object.
  2. Calculate the probability that he was born after the 152nd day of the year (the 1st of June). With the parameters:
    • The lower bound is 1.
    • The upper bound is 365.
  3. Calculate the probability that he was born before the 243rd day of the year (the 31st of August). With the parameters:
    • The lower bound is 1.
    • The upper bound is 365.
  4. Calculate the probability that he was born before the 243rd day of the year and after the 152nd day of the year.

Завдання

Imagine that you met a person and want to calculate the probability of his birthday in summer, you know he wasn't born on a leap year. So, follow the algorithm:

  1. Import uniform object.
  2. Calculate the probability that he was born after the 152nd day of the year (the 1st of June). With the parameters:
    • The lower bound is 1.
    • The upper bound is 365.
  3. Calculate the probability that he was born before the 243rd day of the year (the 31st of August). With the parameters:
    • The lower bound is 1.
    • The upper bound is 365.
  4. Calculate the probability that he was born before the 243rd day of the year and after the 152nd day of the year.

Все було зрозуміло?

Секція 4. Розділ 2
toggle bottom row

Обчислити захоплюючу ймовірність

Have you ever wonder that your friends birthday could be any day of the year with equal probability. The probability for each day creates uniform distribution.

Let's recall some functions, but for the uniform distribution (they are a little bit different): For calculating the probability of receiving exactly defined output x :

uniform.pdf(x, loc, scale).

For calculating the probability of receiving output that is bigger than x:

uniform.sf(x, loc, scale)(inclusive).

For calculating the probability of receiving output that is less than x:

uniform.cdf(x, loc, scale)(inclusive).

  • loc is the lower bound of the distribution (minimum value).
  • scale is the upper bound of the distribution (maximum value).

Завдання

Imagine that you met a person and want to calculate the probability of his birthday in summer, you know he wasn't born on a leap year. So, follow the algorithm:

  1. Import uniform object.
  2. Calculate the probability that he was born after the 152nd day of the year (the 1st of June). With the parameters:
    • The lower bound is 1.
    • The upper bound is 365.
  3. Calculate the probability that he was born before the 243rd day of the year (the 31st of August). With the parameters:
    • The lower bound is 1.
    • The upper bound is 365.
  4. Calculate the probability that he was born before the 243rd day of the year and after the 152nd day of the year.

Завдання

Imagine that you met a person and want to calculate the probability of his birthday in summer, you know he wasn't born on a leap year. So, follow the algorithm:

  1. Import uniform object.
  2. Calculate the probability that he was born after the 152nd day of the year (the 1st of June). With the parameters:
    • The lower bound is 1.
    • The upper bound is 365.
  3. Calculate the probability that he was born before the 243rd day of the year (the 31st of August). With the parameters:
    • The lower bound is 1.
    • The upper bound is 365.
  4. Calculate the probability that he was born before the 243rd day of the year and after the 152nd day of the year.

Все було зрозуміло?

Секція 4. Розділ 2
toggle bottom row

Обчислити захоплюючу ймовірність

Have you ever wonder that your friends birthday could be any day of the year with equal probability. The probability for each day creates uniform distribution.

Let's recall some functions, but for the uniform distribution (they are a little bit different): For calculating the probability of receiving exactly defined output x :

uniform.pdf(x, loc, scale).

For calculating the probability of receiving output that is bigger than x:

uniform.sf(x, loc, scale)(inclusive).

For calculating the probability of receiving output that is less than x:

uniform.cdf(x, loc, scale)(inclusive).

  • loc is the lower bound of the distribution (minimum value).
  • scale is the upper bound of the distribution (maximum value).

Завдання

Imagine that you met a person and want to calculate the probability of his birthday in summer, you know he wasn't born on a leap year. So, follow the algorithm:

  1. Import uniform object.
  2. Calculate the probability that he was born after the 152nd day of the year (the 1st of June). With the parameters:
    • The lower bound is 1.
    • The upper bound is 365.
  3. Calculate the probability that he was born before the 243rd day of the year (the 31st of August). With the parameters:
    • The lower bound is 1.
    • The upper bound is 365.
  4. Calculate the probability that he was born before the 243rd day of the year and after the 152nd day of the year.

Завдання

Imagine that you met a person and want to calculate the probability of his birthday in summer, you know he wasn't born on a leap year. So, follow the algorithm:

  1. Import uniform object.
  2. Calculate the probability that he was born after the 152nd day of the year (the 1st of June). With the parameters:
    • The lower bound is 1.
    • The upper bound is 365.
  3. Calculate the probability that he was born before the 243rd day of the year (the 31st of August). With the parameters:
    • The lower bound is 1.
    • The upper bound is 365.
  4. Calculate the probability that he was born before the 243rd day of the year and after the 152nd day of the year.

Все було зрозуміло?

Have you ever wonder that your friends birthday could be any day of the year with equal probability. The probability for each day creates uniform distribution.

Let's recall some functions, but for the uniform distribution (they are a little bit different): For calculating the probability of receiving exactly defined output x :

uniform.pdf(x, loc, scale).

For calculating the probability of receiving output that is bigger than x:

uniform.sf(x, loc, scale)(inclusive).

For calculating the probability of receiving output that is less than x:

uniform.cdf(x, loc, scale)(inclusive).

  • loc is the lower bound of the distribution (minimum value).
  • scale is the upper bound of the distribution (maximum value).

Завдання

Imagine that you met a person and want to calculate the probability of his birthday in summer, you know he wasn't born on a leap year. So, follow the algorithm:

  1. Import uniform object.
  2. Calculate the probability that he was born after the 152nd day of the year (the 1st of June). With the parameters:
    • The lower bound is 1.
    • The upper bound is 365.
  3. Calculate the probability that he was born before the 243rd day of the year (the 31st of August). With the parameters:
    • The lower bound is 1.
    • The upper bound is 365.
  4. Calculate the probability that he was born before the 243rd day of the year and after the 152nd day of the year.
Секція 4. Розділ 2
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