Probability Distributions
Normal distribution, binomial distribution, and expected value
lessons (10)
Introduction to Probability Distributions
Learn what probability distributions are and how they describe the likelihood of different outcomes.
Binomial Probability
Learn to calculate probabilities when an experiment has exactly two outcomes and is repeated multiple times.
Discrete vs Continuous Distributions
Learn the difference between discrete and continuous probability distributions, and when to use each type.
Expected Value
Learn how to calculate the average outcome of a random event over many trials.
Introduction to Normal Distribution
Learn about the bell curve, the most important probability distribution in statistics.
Binomial Distribution
Learn how to calculate probabilities for repeated independent trials with two outcomes.
Z-Scores
Learn what a z-score tells you, how to calculate it, how to turn it back into a value, and how to compare results from different tests.
Standard Normal Distribution
Learn the standard normal distribution N(0, 1), how to standardize any normal variable and how to read a z-table for left, right and between areas.
Normal Probability
Find probabilities and percentiles for normal data in real units: standardize, read the z-table, and work backwards to cut-off values.
Sampling Distributions
Learn how sample means and sample proportions vary from sample to sample, what the standard error is, and why the central limit theorem makes them approximately normal.
Probability distributions describe how probabilities are spread across possible outcomes. From discrete distributions like binomial to continuous distributions like normal, these models are essential for statistics and data science.
What Students Will Learn
- Understand discrete vs continuous distributions
- Apply the binomial distribution
- Understand the normal distribution
- Use z-scores for normal distributions
- Apply distributions to real problems
Frequently Asked Questions
What is a probability distribution?
A function that gives the probability of each possible outcome. The sum (discrete) or integral (continuous) of all probabilities is 1.
What is the normal distribution?
The bell curve, symmetric about the mean. About 68% of data falls within 1 standard deviation, 95% within 2, and 99.7% within 3.
What is a z-score?
The number of standard deviations a value is from the mean: z = (x - μ)/σ. It lets you compare values from different normal distributions.