Random variables and their distributions are the best tools we have for quantifying and understanding unpredictability. This course covers their essential concepts as well as a range of topics aimed to help you master the fundamental mathematics of chance.
Upon completing this course, you'll have the means to extract useful information from the randomness pervading the world around us.
What makes a variable random?
The language of random variables: independence, distributions, and more.
Know what outcome to expect when you're dealing with randomness.
Use averages to make predictions about random events.
Gain hands-on experience with expectation value by exploring real-world applications.
Practice refining your expectations based on new information.
Explore the most important feature of the expected value.
It's the mathematical way to describe how erratic your random variable is.
Develop an important means for assessing expected values.
Calculate the spread of possibilities for a range of real-world scenarios.
Learn how to measure how two variables influence each other.
Use these models to connect the theory to the real-world.
In this type of distribution, all outcomes are equally likely.
Investigate what surveys and coin flips have in common.
Apply the technique of Bernoulli trials to challenging probability problems.
Discover what it means for a distribution to have "no memory."
When the world gets continuous, calculus meets probability.
Understand what it means for a random variable to have uncountably many outcomes.
Extend the rules of probability to the infinite.
Make sense of the uncertainty in two continuous random variables.
Calculate predictions for uncountable outcomes and learn how to judge their accuracy.
模型的高度,股票,或其他任何东西with these distributions.
Learn about a type of continuous distribution that you see pop up everywhere!
Discover why there's a common distribution for radioactivity and for winning the lottery.
Explore a distribution used by insurance companies the world over.
Learn to model stock market fluctuations in a simple way.