## Binomial, Poisson, and Multinomial Distributions

First, we will talk about binomial probabilities, how to compute their cumulatives, and the mean and standard deviation. Then, we will introduce the Poisson probability formula, define multinomial outcomes, and discuss how to compute probabilities by using the multinomial distribution.

1. A binomial distribution has only two possible outcomes. You can think of them as successes and failures. For the correct answers, the successes are: a flip of heads, a win for Susan, a group member who has passed the midterm, and a correct answer on a multiple-choice question.

2. You may use the Binomial Calculator $(n = 10, p = .5, > or = 8)$. Otherwise add up the probability of getting 8, 9, and 10 heads: .044 + .01 + .001 = .055

3. Use the Binomial Calculator $(n = 20, p = .3, > or = 8). p = .23$

4. Use the Binomial Calculator ($n = 20, p = .3$, less than or $= 3)$. $p = .11$

5. $M = np = 20 \times .3 = 6$

6. $Var = np(1-p) = 50(.6)(1-.6) = 12$