Consider the binomial distribution with n trials and PS) - p.(a) Show that Ply)Ply - 1)(n - y+1)pfor y - 1, 2,..., n. Equivalently, for y- 1, 2, .., n, the equation plv) - M-Y+ 1)P ply - 1) gves a recursive relationship between the probabilities assodated with successive values of Y.Ply - 1)" pr-g- -1)- In-y+ 1)p(b) fn- 70 and p- 0.04, use the above relationship to find PY < 3). (Round your answer to four decimal places.)xPly)Ply - 1)I-+1IP,1fy< (n + 1)p. This establishes that p(y) > ply - 1) if y is smalI (y < (n + 1)p) and p(y) < ply - 1) if y is large (y > (n + 1) p). Thus, successive binamial probabilities increase for a while and decrease from then on.(c) Show thatya(n + 1)p > y(n +1- vp >y+(n +1- vo>Your answer cannot be undenstood or graded. More Information(n+1-yIP>yaplv)Ply - 1)<1 if y > (n + 1) p.Show that(n + 1lp Ply - 2) >..Also for y 2 (n + 1p, then ply) a> ply + 2) >.... Thus it is clear that p(y) is madimized when y is as clase topas possible.

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Consider the binomial distribution with n trials and AS) - p. (a) Show that Ply) Dly- 1) (n-v+ 1P for y- 1. 2.....n. Ecuivalently, for y- 1, 2, n, the equation pty) AEyP ply - 1) gives a recursive relationship between the probablities assodiated with successive values of Y. va Ply- 1) (," Jor - g-- 1) - n-y+ 1p (b) n- 70 and p- 0.04, use the above relationship to find PY < 3). (Round your answer to four decimal places.)

Consider the binomial distribution with n trials and AS) - p. (a) Show that Ply) Dly- 1) (n-v+ 1P for y- 1. 2.....n. Ecuivalently, for y- 1, 2, n, the equation pty) AEyP ply - 1) gives a recursive relationship between the probablities assodiated with successive values of Y. va Ply- 1) (," Jor - g-- 1) - n-y+ 1p (b) n- 70 and p- 0.04, use the above relationship to find PY < 3). (Round your answer to four decimal places.)

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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