Discrete random variables and the binomial distribution
Discrete random variables and the binomial distribution for IB Analysis and Approaches HL, with worked IB exam questions.
A random variable assigns a number to each outcome of a random experiment: the points on a die, the red balls drawn from a bag, the students who pass. When it can only take isolated values (0, 1, 2, …) it is discrete, and it is described by a table giving the probability of each value. From that table you obtain the expected value (the long-run average), the variance and the standard deviation, and with them you can decide whether a game is fair. A special case, which appears in almost every exam, is the binomial distribution: repeating a trial times with two outcomes, success or failure, always with the same probability . In Paper 2 almost everything is done with the graphic display calculator, but you must know how to set up the model correctly and interpret the result.
Recommended order
Follow the sections in order: discrete random variable and its distribution, expected value, variance and games, the binomial distribution and binomial: cumulative probabilities, parameters and problems. At the end you have the IB exam questions grouped by type.
Probability (topic 14), combinations $\binom{n}{r}$ and basic use of a graphic display calculator (GDC).
Sections in this topic
Discrete random variable and its probability distribution
What a discrete random variable is, its probability table, probabilities summing to 1 and cumulative probabilities. IB Analysis and Approaches HL.
3 worked examples Section 2Expected value, variance and fair games
Expected value E(X), variance and standard deviation of a discrete variable, and when a game is fair. IB Analysis and Approaches HL.
3 worked examples Section 3The binomial distribution B(n, p)
When a variable is B(n,p), how to find P(X=k) with the formula and the GDC, and what its graph looks like. IB Analysis and Approaches HL.
3 worked examples Section 4Binomial: cumulative probabilities, expected value and finding n or p
Mean np and variance np(1-p) of the binomial, cumulative probabilities, at least one, and finding n or p with the GDC. IB Analysis and Approaches HL.
3 worked examples End of topicIB exam questions: topic 15
IB exam questions on discrete random variables and the binomial distribution: distributions, expected value, fair games, with solutions.
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