2.Suppose that Y is a binomial random variable based on n trials with success probability p andconsider Y* = n - Y.a Argue that for y* = 0, 1, ..., nP(Y* = y*) = P(n − Y = y*) = P(Y = n − y*).b Use the result from part (a) to show thatnP(Y* = y*) = · ( ₁₁² y.)pª²-xq" = ("₁. )¶" p²-x.- y*c The result in part (b) implies that Y* has a binomial distribution based on n trials and"success" probability p* = q = 1 – p. Why is this result "obvious"?

a) To show that for , we can use the properties of the binomial distribution.Y is a binomial random…

2. Suppose that Y is a binomial random variable based on n trials with success probability p and consider Y*=n-Y. a Argue that for y* = 0, 1,..., n P(Y* = y*) = P(n − Y = y*) = P(Y = n − y*). b Use the result from part (a) to show that n P(Y* = y*) = = (₁ " y₁) p^-' q²" = (".)q" p²-x. n-y* c The result in part (b) implies that Y* has a binomial distribution based on n trials and "success" probability p* = q = 1 - p. Why is this result "obvious"?

2. Suppose that Y is a binomial random variable based on n trials with success probability p and consider Y=n-Y. a Argue that for y = 0, 1,..., n P(Y* = y) = P(n − Y = y) = P(Y = n − y). b Use the result from part (a) to show that n P(Y = y) = = (₁ " y₁) p^-' q²" = (".)q" p²-x. n-y c The result in part (b) implies that Y* has a binomial distribution based on n trials and "success" probability p* = q = 1 - p. Why is this result "obvious"?

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Counting And Probability

Section9.3: Binomial Probability

Problem 2E: If a binomial experiment has probability p success, then the probability of failure is...

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