Chapter 16: Probability Models

Question 1

Bernoulli Trials (Binomial)

Answer 1

1. Only two possible outcomes (binary): success/failure
2. Probability of success is the same on every trial and is denoted by p; probability of failure is denoted by q=1-p
3. Each trials of a random process is independent; Bernoulli trials are based on a single trial

Question 2

Binomial Distribution Conditions

Answer 2

Binary - success/fail
Independent trials
Number of trials is fixed (n)
Same probability of success (p)

Question 3

Binomial Random Variable

Answer 3

Random variable X = the number of successes in a binomial setting

Question 4

Binomial Distribution

Answer 4

The probability distribution of a binomial random variable X

Question 5

Binompdf By-Hand Formula

Answer 5

P(X=x) = nCxp^x(1-p)^(n-x)

Question 6

Mean Of A Binomial Random Variable

Answer 6

μ=np

Question 7

Standard Deviation Of A Binomial Random Variable

Answer 7

σ=squareroot(np[1-p])

Question 8

Normal Model Approximation Of Binomial Model

Answer 8

A normal model N(μ,σ) would be appropriate to approximate a binomial model B(μ,σ) if and only if np≥10 and nq≥10 (np = # of successes, nq = # of failures)

Question 9

Geometric Distribution Conditions

Answer 9

Binary - success/failure
Independent trials of the same random process
First success
Same probability of success (p)

Question 10

Mean Of A Geometric Random Variable

Answer 10

μ=1/p

Question 11

Standard Deviation Of A Geometric Random Variable

Answer 11

σ=(squareroot[1-p])/p

Question 12

Binomial Mean Interpretation

Answer 12

“After many, many trials the average # of [success context] out of [n] is [μX].”

Question 13

Binomial Standard Deviation Interpretation

Answer 13

“The number of [success context] out of [n] typically varies by [σX] from the mean of [μX].”