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Negative binomial distribution
- Intro Lesson16:20
- Lesson: 111:11
- Lesson: 28:20
- Lesson: 38:28
Negative binomial distribution
Lessons
• Negative Binomial Distribution: P(n)=(n−1)C(x−1)px(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 nth 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 nth trial
- Introduction
• Deriving negative binomial distribution
• Formula for negative binomial distribution
• Relation of geometric distribution to the negative binomial distribution - 1.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? - 2.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? - 3.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?