Statistics Quest

Probability Distributions

The models behind data and inference, from the binomial to the F distribution.

Random variables, the Bernoulli, binomial, geometric, hypergeometric and Poisson distributions, the uniform, exponential and normal distributions, and the t, chi-square and F distributions used in inference — with interactive tools that recompute probabilities and quantiles.

Lessons

  1. 1Random variables and their distributionsDescribe a random variable with its pmf or pdf and cdf, and calculate its mean, variance and standard deviation.30 minFree
  2. 2Bernoulli and binomial distributionsRecognise when a count follows a binomial distribution and calculate its probabilities, mean and standard deviation.35 minMembers
  3. 3Geometric and hypergeometric distributionsModel the wait for a first success with the geometric distribution and sampling without replacement with the hypergeometric distribution, and know when the binomial is a safe shortcut.30 minMembers
  4. 4The Poisson distributionCalculate Poisson probabilities for counts in an interval, scale the rate to the interval length, and check whether count data really behave like a Poisson model.35 minMembers
  5. 5Uniform and exponential distributionsCalculate probabilities, means and standard deviations for the continuous uniform and exponential distributions, and judge when an exponential waiting-time model is reasonable.30 minMembers
  6. 6The normal distributionDescribe the normal distribution through its mean and standard deviation, apply the 68–95–99.7 rule, and calculate normal probabilities as areas.30 minMembers
  7. 7Standardising and normal calculationsConvert values to z-scores and use the standard normal distribution to solve forward (value → probability) and inverse (probability → value) problems.30 minMembers
  8. 8The t, chi-square and F distributionsExplain where the t, chi-square and F distributions come from, choose their degrees of freedom, and calculate tail probabilities with them.30 minMembers
  9. 9Quantiles and inverse probabilityFind quantiles of continuous and discrete distributions, and use them as critical values for one- and two-tailed procedures.30 minMembers
  10. 10Choosing and checking a distributionMatch a situation to a suitable probability model, check the model against data, and judge when the normal approximation to the binomial can be trusted.35 minMembers