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Let X ~ Bin(n, p). Show that if x is an integer between 1 and n inclusive, then a. P(X = x) P(X = x- 1) (2+1)() - x + b. Show that if X - Bin(n, p), the most probable value for X is the greatest integer less than or equal to np + p. [Hint: Use part (a) to show that P(X = x) 2 P(X = x - 1) if and only if x < np + p.]

Let X ~ Bin(n, p). Show that if x is an integer between 1 and n inclusive, then a. P(X = x) P(X = x- 1) (2+1)() - x + b. Show that if X - Bin(n, p), the most probable value for X is the greatest integer less than or equal to np + p. [Hint: Use part (a) to show that P(X = x) 2 P(X = x - 1) if and only if x < np + p.]

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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Let X ~ Bin(n, p). Show that if x is an integer between 1 and n inclusive, then a. P(X = x) P(X = x- 1) (2+1)() - x + b. Show that if X - Bin(n, p), the most probable value for X is the greatest integer less than or equal to np + p. [Hint: Use part (a) to show that P(X = x) 2 P(X = x - 1) if and only if x < np + p.]
Transcribed Image Text:Let X ~ Bin(n, p). Show that if x is an integer between 1 and n inclusive, then a. P(X = x) P(X = x- 1) (2+1)() - x + b. Show that if X - Bin(n, p), the most probable value for X is the greatest integer less than or equal to np + p. [Hint: Use part (a) to show that P(X = x) 2 P(X = x - 1) if and only if x < np + p.]
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