Зміст курсу

Probability Theory Basics

1. Basic Concepts of Probability Theory

Stochastic Experiment and Random Event Probability and It's Properties Geometrical Probability Challenge: Solving the Task Using Geometric Probability Independence and Incompatibility of Random Events Conditional Probability

2. Probability of Complex Events

Inclusion-Exclusion Principle Challenge: Solving the Task Using Inclusion-Exclusion Principle The Multiplication Rule of Probability Law of Total Probability Bayes' Theorem Challenge: Solving the Task Using Bayes' Theorem

3. Commonly Used Discrete Distributions

Binomial Distribution Challenge: Solving Task Using Binomial Distribution Multinomial Distribution Geometric Distribution Poisson Distribution Challenge: Solving Task Using Poisson Distribution

4. Commonly Used Continuous Distributions

Continuous Uniform Distribution Exponential Distribution Challenge: Solving Task Using Exponential Distribution Gaussian Distribution Challenge: Solving Task Using Gaussian Distribution

5. Covariance and Correlation

What is Covariance?What is Correlation?Challenge: Solving the Task Using Correlation

Challenge: Solving Task Using Gaussian Distribution

Завдання

Suppose you are going fishing.
One type of fish is well caught at atmospheric pressure from 740 to 760 mm Hg.
Fish of the second species is well caught at a pressure of 750 to 770 mm Hg.

Calculate the probability that the fishing will be successful if the atmospheric pressure is Gaussian distributed with a mean of 760 mm and a mean deviation of 15 mm.

You have to:

Calculate the probability that pressure is in the [740, 760] range.
Calculate the probability that pressure is in the [750, 770] range.
As our events intersect, we must use the inclusive-exclusive principle. Calculate the probability that pressure falls into the intersection of corresponding intervals.

Завдання

Suppose you are going fishing.
One type of fish is well caught at atmospheric pressure from 740 to 760 mm Hg.
Fish of the second species is well caught at a pressure of 750 to 770 mm Hg.

Calculate the probability that the fishing will be successful if the atmospheric pressure is Gaussian distributed with a mean of 760 mm and a mean deviation of 15 mm.

You have to:

Calculate the probability that pressure is in the [740, 760] range.
Calculate the probability that pressure is in the [750, 770] range.
As our events intersect, we must use the inclusive-exclusive principle. Calculate the probability that pressure falls into the intersection of corresponding intervals.

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

Все було зрозуміло?

Секція 4. Розділ 5

Challenge: Solving Task Using Gaussian Distribution

Завдання

Suppose you are going fishing.
One type of fish is well caught at atmospheric pressure from 740 to 760 mm Hg.
Fish of the second species is well caught at a pressure of 750 to 770 mm Hg.

Calculate the probability that the fishing will be successful if the atmospheric pressure is Gaussian distributed with a mean of 760 mm and a mean deviation of 15 mm.

You have to:

Calculate the probability that pressure is in the [740, 760] range.
Calculate the probability that pressure is in the [750, 770] range.
As our events intersect, we must use the inclusive-exclusive principle. Calculate the probability that pressure falls into the intersection of corresponding intervals.

Завдання

Suppose you are going fishing.
One type of fish is well caught at atmospheric pressure from 740 to 760 mm Hg.
Fish of the second species is well caught at a pressure of 750 to 770 mm Hg.

Calculate the probability that the fishing will be successful if the atmospheric pressure is Gaussian distributed with a mean of 760 mm and a mean deviation of 15 mm.

You have to:

Calculate the probability that pressure is in the [740, 760] range.
Calculate the probability that pressure is in the [750, 770] range.
As our events intersect, we must use the inclusive-exclusive principle. Calculate the probability that pressure falls into the intersection of corresponding intervals.

Все було зрозуміло?

Секція 4. Розділ 5

Challenge: Solving Task Using Gaussian Distribution

Завдання

Suppose you are going fishing.
One type of fish is well caught at atmospheric pressure from 740 to 760 mm Hg.
Fish of the second species is well caught at a pressure of 750 to 770 mm Hg.

Calculate the probability that the fishing will be successful if the atmospheric pressure is Gaussian distributed with a mean of 760 mm and a mean deviation of 15 mm.

You have to:

Calculate the probability that pressure is in the [740, 760] range.
Calculate the probability that pressure is in the [750, 770] range.
As our events intersect, we must use the inclusive-exclusive principle. Calculate the probability that pressure falls into the intersection of corresponding intervals.

Завдання

Suppose you are going fishing.
One type of fish is well caught at atmospheric pressure from 740 to 760 mm Hg.
Fish of the second species is well caught at a pressure of 750 to 770 mm Hg.

Calculate the probability that the fishing will be successful if the atmospheric pressure is Gaussian distributed with a mean of 760 mm and a mean deviation of 15 mm.

You have to:

Calculate the probability that pressure is in the [740, 760] range.
Calculate the probability that pressure is in the [750, 770] range.
As our events intersect, we must use the inclusive-exclusive principle. Calculate the probability that pressure falls into the intersection of corresponding intervals.

Все було зрозуміло?

Завдання

Suppose you are going fishing.
One type of fish is well caught at atmospheric pressure from 740 to 760 mm Hg.
Fish of the second species is well caught at a pressure of 750 to 770 mm Hg.

Calculate the probability that the fishing will be successful if the atmospheric pressure is Gaussian distributed with a mean of 760 mm and a mean deviation of 15 mm.

You have to:

Calculate the probability that pressure is in the [740, 760] range.
Calculate the probability that pressure is in the [750, 770] range.
As our events intersect, we must use the inclusive-exclusive principle. Calculate the probability that pressure falls into the intersection of corresponding intervals.

Секція 4. Розділ 5