Statistics 6501, Winter 2009 1

Probability Examples

System Problems: In series, In parallel Suppose a system consists of components connected in series. The system fails if any one of the components fails. If there are n independent components and each fails with probability p,

1. what is the probability that the system will fail?

2. Suppose the system of comments is connected in parallel, what is the probability the system will fail?

3. Draw diagrams that accurately represent the systems.

Birthday Problem Simulation Simulate birthdays b = sample(1:365,25, repl = T) Check matches x = 25 - length(unique(b)) Hardy-Weinberg Law See Problems 72 and 73.