Discrete random variables and the binomial distribution
Discrete random variables, probability distributions, expectation, variance and the binomial distribution for IB Applications SL, with worked exam questions.
A discrete random variable converts the outcome of an experiment into a number (how many heads come up, how many customers arrive, how much is won in a game), and the probability distribution says with what probability it takes each value. From it the expected value (the long-run mean) and the variance are calculated. The most important case in the exam is the binomial distribution , which models the number of successes in independent repetitions of the same experiment. In the IB almost everything is solved with the graphic display calculator, so the essential thing is to recognise the model, write the variable correctly and know what to ask the calculator.
Recommended order
Follow the sections in order: discrete random variable and its distribution, expected value and variance and finally the binomial distribution. At the end you have the IB exam questions grouped by type.
Probability (topic 10).
Sections in this topic
Discrete random variable and probability distribution
What a discrete random variable is, how to build its probability table, why probabilities must sum to 1 and how to calculate them. IB Applications SL.
3 worked examples Section 2Expected value, variance and standard deviation of a discrete variable
How to calculate E(X), the variance and the standard deviation of a discrete random variable, and when a game is fair, with the GDC. IB Applications SL.
3 worked examples Section 3The binomial distribution: probabilities, mean and variance
Recognising a binomial variable B(n,p), calculating P(X=k), P(X≤k) and P(X≥k) with the calculator, and the mean np and variance np(1-p). IB SL.
3 worked examples End of topicIB exam questions for topic 11
IB exam questions on discrete random variables and the binomial: distributions, expected value, variance, with step-by-step solutions.
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