11 In this question, take the number n of stages of a binomial variable X~ B(n, p) to be fixed, and allow p to vary. a Find o as a quadratic in p, and graph it. b Explain the symmetry of the graph. c Show that o< np and o²

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 63RE
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d,e o

11 In this question, take the number n of stages of a binomial variable X ~ B (n,p) to be fixed, and allow p
to vary.
a Find o as a quadratic in p, and graph it.
b Explain the symmetry of the graph.
c Show that o² < np and o² < nq.
n
d Show that the maximum value of o² is 1
4
e Let n be fixed. Show that o →
→ 0 as p
→ 0+ and as p→ 1.
Transcribed Image Text:11 In this question, take the number n of stages of a binomial variable X ~ B (n,p) to be fixed, and allow p to vary. a Find o as a quadratic in p, and graph it. b Explain the symmetry of the graph. c Show that o² < np and o² < nq. n d Show that the maximum value of o² is 1 4 e Let n be fixed. Show that o → → 0 as p → 0+ and as p→ 1.
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