Coaching Centre
Chapter 8: The binomial distribution Notes
Bernoulli trials, binomial probabilities, the mean and variance of binomial distributions, and the distribution of sample proportions with its normal approximation.
Sections
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8A Bernoulli trials and binomial probability Mastered
Bernoulli trials with two outcomes, binomial experiments with repeated independent trials, the binomial probability formula P(X = k) = nCk p^k q^(nāk), and probabilities of at least one and at most one success.
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8B Mean and variance of the binomial distribution Mastered
The notation X ~ Bin(n, p), the mean and variance of a Bernoulli distribution, the mean np and variance np(1 ā p) of a binomial distribution, and finding n and p from a given mean and variance.
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8C Sample proportions and the normal approximation Mastered
Populations and samples, the sample proportion p-hat, its mean p and standard deviation ā(p(1 ā p)/n), the central limit theorem, the normal approximation for large samples, and the effect of sample size.