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

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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.

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