Quartz 4

Population and Sample

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Population

Set of all the possible observations that a random variable 𝑋 can take.

Random Sample

Let 𝑋 be a random variable with a distribution function 𝑓(𝑥), mean 𝜇 and variance 𝜎2. A random sample of size 𝑛 is a set of 𝑛 random variables 𝑋1,𝑋2,𝑋3,…,𝑋𝑛 that satisfy:

  • Let 𝑖∈{1,2,3,…,𝑛} then 𝑋𝑖 has the same distribution of 𝑋: 𝐹𝑋𝑖(𝑥)=𝐹𝑋(𝑥), ∀𝑥∈{1,2,3,…,𝑛}

  • The random variables are independent: 𝐸(𝑋𝑖)=𝜇𝑋, Var(𝑋𝑖)=𝜎2𝑋

Note

The previous definition only applies with aninfinite population or where the sample sizes are to small compare to the population.

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