Probability & Statistics
Probability and Statistics is the largest mathematics section of GATE DA. These lessons go from counting and Bayes' theorem to the normal, t and chi-squared distributions, confidence intervals and z, t and chi-squared tests. Every probability is checked by exact enumeration or a small program, so the numbers in the lessons and answers can be trusted.
1Probability
2Random Variables
- Random Variables, Expectation and VarianceDiscrete and continuous random variables, pmf, pdf and cdf, expectation and variance and their rules, joint and marginal distributions, covariance and correlation, independence, and conditional expectation, for GATE DA.
- Discrete DistributionsThe Bernoulli, binomial, geometric, Poisson, discrete uniform and hypergeometric distributions, their pmfs, means and variances, the Poisson approximation to the binomial, and the memoryless property, for GATE DA.
- Continuous DistributionsThe uniform, exponential and normal distributions, standardisation and the standard normal table, and the t and chi-squared distributions used in statistical inference, for GATE DA.
3Statistical Inference
- Sampling Distributions and the Central Limit TheoremPopulations and samples, the sample mean and sample variance, unbiased estimators, the standard error, the law of large numbers, and the central limit theorem with worked GATE DA examples.
- Confidence IntervalsPoint and interval estimation, confidence intervals for a mean with known variance (z interval) and unknown variance (t interval), intervals for a proportion, the margin of error, choosing the sample size, and how to interpret a confidence level, for GATE DA.
- Hypothesis Testing - z, t and Chi-Squared TestsNull and alternative hypotheses, test statistics, critical regions and p-values, type I and type II errors and power, the z-test, the one-sample t-test, and the chi-squared goodness-of-fit and independence tests, with worked GATE DA examples.