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.

- A. Generating possible outcomes

- i. letters
- ii. Exponents

- iii. Coefficients

e.g., 2 coins (P + Q) ^{2} = P^{2} + 2PQ + Q^{2}

B. Calculate the probabilities

i. separate and substitute

P^{2}

2PQ

Q^{2}

e.g., 3 coins

(P + Q)^{3} = P^{3} + 3P^{2}Q + 3PQ^{2} + Q^{3}

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