← Apply probability distributions
1 Reading the notation
Statistics distinguishes carefully between what is true of a POPULATION and what you measured in a SAMPLE, and uses different symbols for each.📖 Symbols used in probability distributions
8 termsCover the right column and check you can say what each one means.
- μ (mu)
- The population mean, the true average of the whole population, usually unknown. The sample mean is written x̄ ("x-bar"). Greek = population, Roman = sample.
- σ (sigma, lower case)
- The population standard deviation. σ² is the variance. The sample standard deviation is written s.
- Σ (sigma, capital)
- A completely different meaning: “the sum of”. Σx means add up all the x values. Same Greek letter, two unrelated uses. Capital is an instruction to add, lower case is a quantity.
- λ (lambda)
- The mean rate of a Poisson distribution: the average number of events per interval. For Poisson, mean = variance = λ.
- z (z-score)
- How many standard deviations a value sits above (+) or below (−) the mean: z = (x − μ)/σ. Standardising lets you compare values from completely different distributions.
- n and p
- n = number of trials, p = probability of success on one trial. Together they define a binomial distribution.
- P(X = r)
- “The probability that the random variable X takes the value r.” Capital X is the variable; lower-case r is a particular value.
- X ~ B(n, p)
- Read as “X is distributed binomially with n trials and probability p”. The tilde ~ means “is distributed as”. Similarly X ~ N(μ, σ²) means X follows a normal distribution, and X ~ Po(λ) a Poisson one.