9 terms

Conditions for Bernoulli Trials

1. There are two possible outcomes (success and failure).

2. the probability of success, p, is constant.

3. the trails are independent.

Ex. Flipping a coin; rolling a die and noting whether or not it came up as a six.

2. the probability of success, p, is constant.

3. the trails are independent.

Ex. Flipping a coin; rolling a die and noting whether or not it came up as a six.

Geometric probability model

- Tells us the probability for a random variable that counts the number of Bernoulli trials UNTIL THE FIRST SUCCESS

- Denoted by: Geom(p)

- Denoted by: Geom(p)

Mean & Standard Deviation of Geometic model

Mean = 1/p

SD = sqrt(q)/p

SD = sqrt(q)/p

Binomial probability model

- Tells us the probabilty for a random variable that counts the NUMBER OF SUCCESSES in a fixed number of Bernoulli trials.

- Denoted by: Binom(n,p)

- Denoted by: Binom(n,p)

Mean & Standard Deviation of Binomal model

Mean = np

SD = sqrt(npq)

SD = sqrt(npq)

10% Condition

Bernoulli trials must be independent.

It is only okay to proceed if the sample is smaller than 10% of the population.

It is only okay to proceed if the sample is smaller than 10% of the population.

Success/Failure condition

- A binomal model is approximately Normal if we expect at least 10 successes and 10 failures:

np > or equal to 10 and nq > or equal to 10

np > or equal to 10 and nq > or equal to 10

Difference between Geometric and Binomial models

- Both involve Bernoulli trials, but the issues are different.

- Geometric probability = trials until first success

- Binomial probability = number of successes in a specified number of trials

- Geometric probability = trials until first success

- Binomial probability = number of successes in a specified number of trials

Difference between Normal and Binomial models

- Binomial gives probabilities for a specific count

- Normal gives continous random variable that can take place on any value

- Normal gives continous random variable that can take place on any value