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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 as a quadratic in p, and graph it. b Explain the symmetry of the graph. c Show that o< np and o² < nq. Show that the maximum value of of is d

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 as a quadratic in p, and graph it. b Explain the symmetry of the graph. c Show that o< np and o² < nq. Show that the maximum value of of is d

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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A,b,c 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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