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• Negative Binomial Distribution: $P(n)=_{(n-1)}C_{(x-1)}p^x(1-p)^{n-x}$

$n$: number of trials

$x$: number of success in n trials

$p$: probability of success in each trial

$P(n)$: probability of getting the $x$ success on the $n^{th}$ trial

$n$: number of trials

$x$: number of success in n trials

$p$: probability of success in each trial

$P(n)$: probability of getting the $x$ success on the $n^{th}$ trial

- 1.

• Deriving negative binomial distribution

• Formula for negative binomial distribution

• Relation of geometric distribution to the negative binomial distribution - 2.
**Identifying Negative Binomial Distributions**

Identify which of the following experiments below are negative binomial distributions?

i. A fair coin is flipped until head comes up 4 times. What is the probability that the coin will be flipped exactly 6 times?

ii. Cards are drawn out of a deck until 2 exactly aces are drawn. What is the probability that a total of 10 cards will be drawn?

iii. An urn contains 3 red balls and 2 black balls. If 2 balls are drawn with replacement what is the probability that 1 of them will be black?

iv. Roll a die until the first six comes up. What is the probability that this will take 3 rolls? - 3.
**Determining the Negative Binomial Distribution**

A fair coin is flipped until head comes up 4 times. What is the probability that the coin will be flipped exactly 6 times? - 4.
**Determining the Cumulative Negative Binomial Distribution**

A sculptor is making 3 exhibits for an art gallery. There is a probability of 0.75 that every piece of wood she carves into will be good enough to be part of the exhibit. What is the probability that she uses 4 pieces of wood or less?

4.

Discrete Probabilities

4.1

Probability distribution - histogram, mean, variance & standard deviation

4.2

Binomial distribution

4.3

Mean and standard deviation of binomial distribution

4.4

Poisson distribution

4.5

Geometric distribution

4.6

Negative binomial distribution

4.7

Hypergeometric distribution

4.8

Properties of expectation

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