Probability and Statistics Masterclass - Making maths fun.

Understand what a random variable is through clear examples of discrete and continuous types. See how constants and independent variables interact in a random experiment to produce outcomes.

Discover how percentiles, quartiles and the interquartile range describe data distribution, with the median as the 50th percentile, and learn percentile calculations and the concept of maximum.

Explore the chi-square goodness-of-fit test, defining null and alternative hypotheses, computing the chi-square statistic from observed and expected counts, and assessing fit with degrees of freedom and 5% significance level.

Explore how the probability distribution function represents each value's probability as a graph, with the discrete case using a probability mass function and a fair die example.

Explore continuous random variables and the distribution function, and the probability density function, where the area under the curve between two heights yields probability and the total area equals one.

Explore the binomial distribution as an extension of the Bernoulli model, with independent trials and the binomial formula for exactly k successes in n trials, illustrated by coin flips.

Understand the expected value as the weighted average of outcomes. A gambling example shows how positive value supports playing and relates to the law of large numbers.

Show how standard deviation and variance shape the normal distribution: higher standard deviation flattens the curve, lower standard deviation peaks it, while the area under the curve remains one.

Explore the normal distribution formula, identify its parameters mu and standard deviation, and see how changing these values shapes the curve, with hands-on Excel data experiments.

Explore the normal distribution using an Excel utility to compute pdf and cdf, adjust mu and sigma, and visualize how mean and spread shape the area under the curve.

Learn to read a z score table for a normal distribution, using the z formula (x - μ)/σ, interpreting left and right areas and symmetry to find probabilities.

Calculate the probability of a free pizza using the z score for a normal distribution, with mean 16.3 and standard deviation 0.2, finding the left-tail area below 16 inches.

Use z-scores to infer mu and sigma from 15% below 30 hours and 10% above 50 hours. Solve two linear equations from these z-values and confirm the normal distribution properties.

Explore the log normal distribution and its link to the normal distribution via log and exponentials, and note mu and sigma from the normal curve of log X.

Learn how a Q-Q plot compares an unknown distribution to a known one by pairing ordered quantiles; a straight line indicates they are the same distribution, widely used beyond normality.

Explore the box-cox transformation that converts any distribution toward normality using the lambda parameter, with lambda=0 yielding a log transform. Visualize the results with QQ plots to assess effectiveness.

Construct a 90% confidence interval for mean number of years US companies trade with firms in India, using a 44-sample mean 10.455 and sigma 7.7, per the central limit theorem.

Learn why the z score fails when population std dev is unknown and how the t score, using sample std dev, degrees of freedom, and the t table, replaces it.

Test the null mu=20 against mu<20 using a one-tailed t-test with n=20, x̄=19.8, s=3.1, applying the central limit theorem and interpret p-values to conclude the null cannot be rejected.

Assess a one-tailed hypothesis test for plant growth, using sample mean 11.4, sd 2.5, n=15 to compute t and p value and alpha-driven rejection region.

Examine mutually exclusive and independent events with coin tosses and samples, simplify probability with intersection and union, and apply conditional probability and Bayes theorem to solve problems.

Compute the probability of drawing two blue and two green balls from four blue and three green without replacement, using intuitive sample-space reasoning and mutually exclusive orderings to obtain 18/35.

Explore probability through a three-friend chit problem and a five-day power-cut scenario, analyzing exactly one or none picks their name and at least one power cut using independence.

Explore probability trees to visualize and solve complex problems with diagrams, turning scenarios into clear branches and using conditional probabilities to compute events like watching cricket and seeing ads.

Apply the total law of probability to a travel luggage problem, using conditional probabilities and probability trees to find the chance of luggage arriving in B given on-time or late flights.

Multiply options for legs—Delhi to Mumbai: 8 flights, 12 trains, 2 roadways; Mumbai to Chennai: 6 flights, 10 trains, 2 roadways. Treat the legs as independent and yield 396 ways.

Explore factorial notation, define n factorial as the product 1 through n, show examples like 5! and 3!, and explain how n! equals n times (n minus 1)!, enabling cross-cancellation.

Explore permutation with repetition by counting four-digit arrangements from a repeating set, using nPk divided by repetition factorial, and recognizing when the formula fails, with worked examples.

Examine permutations with repetition using A, B, C. Positions yield 9 arrangements; repeating characters don't affect count when repetition is allowed, with three and four digits giving 27 and 81.

Evaluate two-ball draws from a bag of eight white, three black, two red; assign +10 for black, -2 for white, 0 for red; determine expected value, probabilities, and three-play profitability.

Learn to calculate the probability of at least one power cut over the next three days with a daily 0.05 chance, by summing scenarios or using 1 minus no cuts.