Methodology Solving problems with known distributions 1

General Methodology 1. Define the random variable X 2. Find the distribution of X 3. Find the parameters of the distribution 4. Define the event of interest 5. Solve it 6. Interpret it 2

Binomial Distribution 1. X= « The number of (successes) » 2. X~Bin(n,p) 3. Parameters 1. n= number of trials = p= probability of a success = … 4. P(X=…) or P(X …) or P(X>=…) or P(…<X<…) or … 5. Solve it 6. Interpret it 3

Poisson Distribution 1. X= « The number of (successes) within (t*Unit)» 2. X~P(λt) 3. Parameters 1. Unit = 2. λ = mean = … 3. t = number of units =… 4. P(X=…) or P(X …) or P(X>=…) or P(…<X<…) or … 5. Solve it 6. Interpret it 4

Hypergeometric Distribution 1. X= « The number of (successes) » 2. X~H(N,S,n) 3. Parameters 1. N = size of the population = 2. S = number of successes in the population = … 3. n = size of the sample = … 4. P(X=…) or P(X …) or P(X>=…) or P(…<X<…) or … 5. Solve it 6. Interpret it 5