Consider independent trials, each of which results in outcome i, i = 0, 1, .., k, with probability Pi, where o Pi = 1. Let N denote the number of trials needed to obtain an outcome that is not equal to 0, and let X be that outcome. (a) Find P(N = n), n > 1 %3D (b) Find P(X = j),j = 1, ..., k (c) Show that P(N = n, X = j) = P(N = n)P(X = j)
Consider independent trials, each of which results in outcome i, i = 0, 1, .., k, with probability Pi, where o Pi = 1. Let N denote the number of trials needed to obtain an outcome that is not equal to 0, and let X be that outcome. (a) Find P(N = n), n > 1 %3D (b) Find P(X = j),j = 1, ..., k (c) Show that P(N = n, X = j) = P(N = n)P(X = j)
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
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D5)
Transcribed Image Text:Consider independent trials, each of which results in outcome i, i = 0, 1, ..., k, with probability
Pi, where , Pi = 1. Let N denote the number of trials needed to obtain an outcome that is not equal to
0, and let X be that outcome.
(a) Find P(N = n),n > 1
%3D
(b) Find P(X = j),j = 1, ..., k
(c) Show that P(N = n, X = j) = P(N = n)P(X = j)
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