Track 5 · Probability Distributions · Lesson 2 of 10
Bernoulli and binomial distributions
Recognise when a count follows a binomial distribution and calculate its probabilities, mean and standard deviation.
A quality inspector samples panels from a production line and counts the defective ones; a marketer sends 20 offers and counts how many are accepted. Whenever you count successes in a fixed number of independent yes/no trials with the same chance of success, the binomial distribution tells you how surprised to be by the count you see.
A Bernoulli trial is a single random experiment with two outcomes, called success (coded 1) and failure (coded 0), with . One panel inspected (defective or not), one call (abandoned or not), one customer (buys or not). A Bernoulli variable has mean and variance .
The binomial distribution counts the successes in such trials.
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It has 8 graded exercises with feedback, hints and worked solutions. After it you will be able to:
- Check the four binomial conditions and recognise when a count needs a different model
- Calculate P(X = k), P(X ≤ k), P(X < k) and P(X ≥ k) for a binomial count
- Use μ = np and σ = √(np(1 − p)) to describe a count and judge how unusual an observation is
- Choose a sample size so that a rare event is likely to be observed