Probability and Statistics

Probability and Statistics teaches you probability and statistical inference step by step: 35 lessons in 7 sections, from probability rules and Bayes' theorem to probability distributions, confidence intervals and hypothesis testing.
Every lesson has clear explanations, original drawings, worked examples and practice questions, and the whole app works offline.

Each topic explains the idea first, then the formula with every symbol explained, then a worked example you can follow line by line. All numbers and table values in the examples were computed and checked.

What you will learn

• Probability: sample spaces and events, probability rules (addition, multiplication, complement), conditional probability and independence, Bayes' theorem with tree diagrams, permutations and combinations
• Discrete distributions: random variables and expected value, the binomial distribution, the Poisson distribution and the geometric distribution
• Continuous distributions: uniform and exponential distributions, the normal distribution, the standard normal and the z-table, the normal approximation to the binomial
• Sampling distributions: the sampling distribution of the mean, the central limit theorem, the sampling distribution of a proportion
• Confidence intervals: z-intervals for a mean, the t distribution and t-intervals, confidence intervals for a proportion, margin of error and choosing the sample size
• Hypothesis testing: hypotheses and test logic, p-values and significance, type I and II errors and power, one-sample z-test and t-test, test for a proportion, two-sample t-test, comparing two proportions, paired t-test
• Centre and spread: mean, median and mode, quartiles and IQR, box plots and outliers, variance and standard deviation, z-scores and percentiles, the empirical rule and Chebyshev
• Formulas and tables: a formula sheet, a standard normal (z) table, t critical values and chi-square critical values

Features
• 35 probability and statistics lessons in 7 sections, plus a formula sheet and 3 statistical tables
• 35 original drawings: tree diagrams, probability distributions, normal curves, sampling distributions, confidence intervals and p-value areas
• 60 worked examples with full steps
• 108 practice questions with tap-to-reveal answers
• Formulas with the meaning of each symbol
• Search all probability and statistics topics from the home screen
• Dark mode
• Works offline, no account needed
• Available in 8 languages: English, Español, Português, Français, Deutsch, العربية, हिन्दी and Bahasa Indonesia

Who it is for
• College and university students taking an introductory probability and statistics course
• High school students learning probability and statistics; useful when revising for AP Statistics
• Anyone who wants to understand probability, distributions, p-values and confidence intervals

Probability and Statistics is an independent study aid. Content is based on OpenStax Introductory Statistics (2nd edition) and OpenIntro Statistics (4th edition), with reference values checked against the NIST/SEMATECH e-Handbook of Statistical Methods. It is not affiliated with any exam board, textbook publisher, university or official body.

Recent changes:
Stability improvements.