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We throw a coin until a head turns up for the second time, where p is the probability that a throw results in a head and we assume that the outcome of each throw is independent of the previous outcomes. Let X be the number of times we have thrown the coin. 1) Determine P(X 2), P(X = 3), and P(X = 4). 2) Show that P(X = n) = (n- 1) p (1 – p) 2 for n>= 2

We throw a coin until a head turns up for the second time, where p is the probability that a throw results in a head and we assume that the outcome of each throw is independent of the previous outcomes. Let X be the number of times we have thrown the coin. 1) Determine P(X 2), P(X = 3), and P(X = 4). 2) Show that P(X = n) = (n- 1) p (1 – p) 2 for n>= 2

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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We throw a coin until a head turns up for the second time, where p is the probability that a throw results in a head and we assume that the outcome of each throw is independent of the previous outcomes. Let X be the number of times we have thrown the coin. 1) Determine P(X = 2), P(X = 3), and P(X = 4). 2) Show that P(X = n) = (n – 1) p (1 – p) 2 for n>= 2 n-2
Transcribed Image Text:We throw a coin until a head turns up for the second time, where p is the probability that a throw results in a head and we assume that the outcome of each throw is independent of the previous outcomes. Let X be the number of times we have thrown the coin. 1) Determine P(X = 2), P(X = 3), and P(X = 4). 2) Show that P(X = n) = (n – 1) p (1 – p) 2 for n>= 2 n-2
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