(e) Show that PY) ply - 1) G-y+1)P > 1 if y < (n + 1)p. This establishes that ply) > plY - 1) if y is small y < (n - 1)p) and ply) < Ply - 1) # y is large (y > (n - 1) p). Thus, successive binomial probabilities increase for a while and decrease from then on. (n - 1)p > y (n +1- y)p > y n+1 (n +1- y)p > (n +1- ylp Show that PY <1 if y > (n + 1) p. Py - 1) (n + 1)p ply-2) >... Also for y 2 (n + 1)p, then p(y) zA > p(y + 2) >. Thus it is clear that p(y) is maximized when y is as close to p as possible.
(e) Show that PY) ply - 1) G-y+1)P > 1 if y < (n + 1)p. This establishes that ply) > plY - 1) if y is small y < (n - 1)p) and ply) < Ply - 1) # y is large (y > (n - 1) p). Thus, successive binomial probabilities increase for a while and decrease from then on. (n - 1)p > y (n +1- y)p > y n+1 (n +1- y)p > (n +1- ylp Show that PY <1 if y > (n + 1) p. Py - 1) (n + 1)p ply-2) >... Also for y 2 (n + 1)p, then p(y) zA > p(y + 2) >. Thus it is clear that p(y) is maximized when y is as close to p as possible.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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