Binomial Model

Question 1

Conditions for Binomial Setting

Answer 1

1. There are a fixed number, n, of observations or trials.
2. The n observations are independent.
3. Each observation falls into one of just two categories (‘success’ and ‘failure’)
4. The probability of a success,p, is the same for each observation

Question 2

Binomial Distributions

Answer 2

A class of discrete probability distributions that count (X) successes in a binomial setting.

Question 3

Parameters of Binomial Distribution

Answer 3

Defined by parameters n and p

possible values are whole numbers 0 to n.

Question 4

Binomial model equation

Answer 4

If k is a value of X~BIN(n,p) then,

𝑃(𝑋 = 𝑘)= (n k)p^k(1-p)^n-k

n = number of observations
p = probability of success

Binomial distributions count the number of successes for a fixed number of observation

The probability that the variable takes the values k

Question 5

Let X be the random variable counting the number of students in an SRS of 4 who have a job. Assuming having a job is equally likely as not having a job.
What is the probability that X = 1?

Answer 5

4 ways: YNNN, NYNN, NNYN, NNNY

Question 6

Describing binomial distributions

Answer 6

Probability distributions—including the binomial distributions—can be described in terms of shape, centre, and spread

mean: mu = np

standard deviation= sigma=sqr(np(1-p))
-the larger the standard deviation the more spread out the distribution (sd=0.1, skewed)

We can judge the shape of a binomial distribution based on the probability of success