BINOMIAL DISTRIBUTION

1. Introduction- hypothesis testing

A. Definition: a probability distribution that results when 5 conditions are met:

1) there are a series of N trials,



2) on each trial there are only 2 possible outcomes



3)outcomes are mutually exclusive



4) outcomes are independent



5) the probability of each possible outcome stays the same from trial to trial

2. Outcome of tossing 2 or 3 coins

1. What are the possible outcomes



2. Calculate the probabilities







3. The binomial expansion

(P + Q) N

where P = probability of one of the two possible outcomes

Q = probability of the other possible outcome ( Q = 1-P)

N = number of trials.


e.g., 2 coins (P + Q) 2 = P2 + 2PQ + Q2

B. Calculate the probabilities

i. separate and substitute

P2

2PQ

Q2

e.g., 3 coins

(P + Q)3 = P3 + 3P2Q + 3PQ2 + Q3






4. Binomial problems using Table B

A. N trials



B. number of P or Q events



C. Probability value of P or Q



D. Examples when prob < .05









E. Examples when prob > .05





i. find the probability of Q ie., 1-P.





i i. Then find the number of q events= N-P

Statistics