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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

Поєднуйте свої знання

It is time to deal with three experiments; they are very similar, so firstly, let's recall some theory.

FunctionExplanation
binom.pmf(k, n, p)Calculate the probability to archive exactly k successes among n trials with the probability of success p
binom.sf(k, n, p)Calculate the probability to archive k or more successes among n trials with the probability of success p
binom.cdf(k, n, p)Calculate the probability to archive k or less successes among n trials with the probability of success p

Завдання

Here, it would be best if we coped with several tasks.

  1. Calculate the probability that among 50 unique pictures, exactly 5 have a defect; the probability that a picture has a defect is 25%.
  2. Calculate the probability that at least 9(9 or more) employees are satisfied with their salary if we know that there are 20 workers in the project. The probability for the positive answer is 75% .
  3. Calculate the probability that 6 or fewer thefts this month will be revealed; we know that in the specific city, the amount of thefts is 10. The probability of revealing is 5%.

Завдання

Here, it would be best if we coped with several tasks.

  1. Calculate the probability that among 50 unique pictures, exactly 5 have a defect; the probability that a picture has a defect is 25%.
  2. Calculate the probability that at least 9(9 or more) employees are satisfied with their salary if we know that there are 20 workers in the project. The probability for the positive answer is 75% .
  3. Calculate the probability that 6 or fewer thefts this month will be revealed; we know that in the specific city, the amount of thefts is 10. The probability of revealing is 5%.

Все було зрозуміло?

Секція 3. Розділ 4
toggle bottom row

Поєднуйте свої знання

It is time to deal with three experiments; they are very similar, so firstly, let's recall some theory.

FunctionExplanation
binom.pmf(k, n, p)Calculate the probability to archive exactly k successes among n trials with the probability of success p
binom.sf(k, n, p)Calculate the probability to archive k or more successes among n trials with the probability of success p
binom.cdf(k, n, p)Calculate the probability to archive k or less successes among n trials with the probability of success p

Завдання

Here, it would be best if we coped with several tasks.

  1. Calculate the probability that among 50 unique pictures, exactly 5 have a defect; the probability that a picture has a defect is 25%.
  2. Calculate the probability that at least 9(9 or more) employees are satisfied with their salary if we know that there are 20 workers in the project. The probability for the positive answer is 75% .
  3. Calculate the probability that 6 or fewer thefts this month will be revealed; we know that in the specific city, the amount of thefts is 10. The probability of revealing is 5%.

Завдання

Here, it would be best if we coped with several tasks.

  1. Calculate the probability that among 50 unique pictures, exactly 5 have a defect; the probability that a picture has a defect is 25%.
  2. Calculate the probability that at least 9(9 or more) employees are satisfied with their salary if we know that there are 20 workers in the project. The probability for the positive answer is 75% .
  3. Calculate the probability that 6 or fewer thefts this month will be revealed; we know that in the specific city, the amount of thefts is 10. The probability of revealing is 5%.

Все було зрозуміло?

Секція 3. Розділ 4
toggle bottom row

Поєднуйте свої знання

It is time to deal with three experiments; they are very similar, so firstly, let's recall some theory.

FunctionExplanation
binom.pmf(k, n, p)Calculate the probability to archive exactly k successes among n trials with the probability of success p
binom.sf(k, n, p)Calculate the probability to archive k or more successes among n trials with the probability of success p
binom.cdf(k, n, p)Calculate the probability to archive k or less successes among n trials with the probability of success p

Завдання

Here, it would be best if we coped with several tasks.

  1. Calculate the probability that among 50 unique pictures, exactly 5 have a defect; the probability that a picture has a defect is 25%.
  2. Calculate the probability that at least 9(9 or more) employees are satisfied with their salary if we know that there are 20 workers in the project. The probability for the positive answer is 75% .
  3. Calculate the probability that 6 or fewer thefts this month will be revealed; we know that in the specific city, the amount of thefts is 10. The probability of revealing is 5%.

Завдання

Here, it would be best if we coped with several tasks.

  1. Calculate the probability that among 50 unique pictures, exactly 5 have a defect; the probability that a picture has a defect is 25%.
  2. Calculate the probability that at least 9(9 or more) employees are satisfied with their salary if we know that there are 20 workers in the project. The probability for the positive answer is 75% .
  3. Calculate the probability that 6 or fewer thefts this month will be revealed; we know that in the specific city, the amount of thefts is 10. The probability of revealing is 5%.

Все було зрозуміло?

It is time to deal with three experiments; they are very similar, so firstly, let's recall some theory.

FunctionExplanation
binom.pmf(k, n, p)Calculate the probability to archive exactly k successes among n trials with the probability of success p
binom.sf(k, n, p)Calculate the probability to archive k or more successes among n trials with the probability of success p
binom.cdf(k, n, p)Calculate the probability to archive k or less successes among n trials with the probability of success p

Завдання

Here, it would be best if we coped with several tasks.

  1. Calculate the probability that among 50 unique pictures, exactly 5 have a defect; the probability that a picture has a defect is 25%.
  2. Calculate the probability that at least 9(9 or more) employees are satisfied with their salary if we know that there are 20 workers in the project. The probability for the positive answer is 75% .
  3. Calculate the probability that 6 or fewer thefts this month will be revealed; we know that in the specific city, the amount of thefts is 10. The probability of revealing is 5%.
Секція 3. Розділ 4
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