Binomial distributions

Mathematical Methods · Unit 3 — Further calculus and introduction to statistics · Discrete random variables

Learning objectives (6)

LO-1Calculate the mean 𝑛𝑝 and variance 𝑛𝑝(1 − 𝑝) of a binomial distribution using technology and algebraic methods.LO-2Determine and use the probabilities 𝑃(𝑋 = 𝑟) = (𝑛 𝑟) 𝑝𝑟 (1 − 𝑝)𝑛−𝑟 associated with the binomial distribution with parameters 𝑛 and 𝑝.LO-3Identify contexts suitable for modelling by binomial random variables.LO-4Model and solve problems that involve binomial distributions and associated probabilities with and without technology.LO-5Understand the concepts of Bernoulli trials and the concept of a binomial rand om variable as the number of ‘successes’, 𝑟, in 𝑛 independent Bernoulli trials, with the same probability of success 𝑝 in each trial.LO-6Use the language of probability, including at most, at least, no more than, no less than, inclusive and between.

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