Probability Distributions
Applied Mathematics, Unit IV; simple probability in Section A.
About this unit
This unit treats the outcome of a random experiment as a number, called a random variable, and studies how probability is spread over its values. You learn to write a probability distribution, find its mean (expected value) and its variance and standard deviation. You then meet three standard models used throughout statistics and business: the binomial distribution for counting successes in a fixed number of independent trials, the Poisson distribution for counting rare events in a fixed interval, and the normal distribution, the bell-shaped curve that describes many measurements and is the basis of inferential statistics. Knowing which model fits a situation is as important as the formulas.
How to prepare
- Memorise: E(X) = Σxp, Var(X) = E(X²) − [E(X)]², binomial mean np and variance npq, Poisson mean = variance = λ, Z = (X − μ)/σ.
- Practise checking that probabilities add to 1 before computing anything.
- Learn the 68–95–99.7 rule and how to use symmetry of the normal curve.
- For each word problem, first identify the distribution and its parameters.
Topics in this chapter
Random variables and expectation
Discrete probability distributions and expected value.
5 questionsVariance and standard deviation
Spread of a random variable.
5 questionsBinomial distribution
Bernoulli trials, mean and variance.
5 questionsPoisson distribution
Conditions, mean and variance.
5 questionsNormal distribution
Standard normal variate and areas under the normal curve.
5 questions