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Could you please explain me why an when do I have to use the negative binomial...

Could you please explain me why an when do I have to use the negative binomial distribution for Problem 15 in chapter 2 (rice- mathematical statistics and Data Analysis 3rd Edition). I wanted to use the normal binomial distribution but I come to the wrong results....

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Answer #1

Basically we use binomial distribution when n is fixed .

but here n is not fixed,

whereas

the negative binomial distribution is a discrete probability distribution of the number of successes in a sequence of independent and identically distributed Bernoulli trials before a specified (non-random) number of failures (denoted r) occurs.

here we have to win first 3 games in 5 and first 4 games in 7 .

note that if we win first 3 games , we don't need to play next match.

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