Question

• Population consists of these three numbers 1 2 3 and 4 list all the possible samples of size n = 2 which can be drawn with replacement from the population.

Answer 1

For the population consisting of numbers $1,2,3$ we have the following possible samples: $(1,1),(1,2),(1,3),(2,1),(2,2),(2,3),(3,1),(3,2),(3,3)$. The probability to receive one of these samples (in case every number has the same chance to be chosen) is: $\frac19$. For the population consisting of numbers $1,2,3,4$ we have: $(1,1),(1,2),(1,3),$

$(1,4),(2,1),(2,2),(2,3),(2,4),(3,1),(3,2),(3,3),(3,4),(4,1),(4,2),(4,3),(4,4).$ The possibility to get one of these samples (in case every number has the same chance to be chosen) is: $\frac{1}{16}$