Bonus Group Project 1: Negative Binomial Distribution
Negative Binomial experiment is based on sequences of Bernoulli trials with probability of success p. Let x+m be the number of trials to achieve m successes, and then x has a negative binomial distribution. In summary, negative binomial distribution has the following properties
Given , X+m is the number of trials to achieve mth success (X be the number of failures before mth success) , with probability of success is p
X follow Negative Binomial distribution
The probability distribution of X is given by
Tossing a coin
Let X be the number of failures before the third head ( or X+3 be the number of trials), m=3 , p= 0.5 (probability of head)
To find P(X=3) =?
Probability that 3rd head occurs at 6th toss = 0.15625
Let X+ 10 be the number of house she goes to sells 10 boxes
X follow negative Binomial distribution with m=10 , p =0.6
Probability that she sells the last box at 15th house is 0.12396
Probability that she exhausts 20 houses = 0.05857
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