3.2 Probability and probability distributions notes

1. 3.2.1Conditional probability, independent events, total probability and Bayes' theorem

   Conditional probability P(B | A) is the chance of B after we know A has happened; events are independent when this knowledge changes nothing, the total probability theorem adds up the routes to an event, and Bayes' theorem turns the question around to find which route was taken.

   Advanced · 8 min · Full course
2. 4.1.1Random variables, probability mass and density functions, mathematical expectation and variance

   A random variable gives a number to every outcome of an experiment; its probabilities are described by a mass function (discrete) or a density function (continuous), and its expectation E(X) and variance V(X) are the probability-weighted mean and spread.

   Advanced · 7 min · Read here
3. 4.1.2Bernoulli, binomial and Poisson distributions

   A Bernoulli trial has two outcomes; the binomial B(n, p) counts successes in n independent trials (mean np, variance npq), and the Poisson P(λ) counts rare events (mean = variance = λ) and is the limit of the binomial when n is large and p is small.

   Advanced · 7 min · Read here
4. 4.1.3Normal distribution: properties, standard normal, area rules and uses

   The normal distribution N(μ, σ²) is the symmetric bell-shaped continuous distribution fixed by its mean μ and variance σ²; every normal question is solved by changing X to the standard normal Z = (X − μ)/σ and reading areas from the Z table.

   Advanced · 8 min · Read here

Medha AI is an independent preparation service. It is not affiliated with, endorsed by or connected to APPSC, TGPSC (formerly TSPSC), MPSC, UPSC or any other commission or government body.