Find P(X > x) and show that P(X < 3) = 1-q*. Explain why P[X is odd(= 1,3,5,7, ..)]) = q x P[X is even(= 0,2,4,6, .-.)] And hence otherwise show that P(X is odd) = ; 1+9 Find P(X is odd|X < 3) as a function of q, and, given that
Find P(X > x) and show that P(X < 3) = 1-q*. Explain why P[X is odd(= 1,3,5,7, ..)]) = q x P[X is even(= 0,2,4,6, .-.)] And hence otherwise show that P(X is odd) = ; 1+9 Find P(X is odd|X < 3) as a function of q, and, given that
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 10E
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![The random variable X has the geometric distribution with probability mass function (pmf)
Px (x) = q*p, x = 0, 1, 2, ... 0<p< 1,
where q = 1-p
i)
Find P(X > x) and show that P(X < 3) = 1-q*.
ii)
Explain why
P[X is odd(= 1,3,5,7, ...)] = q x P[X is even(= 0,2,4,6, ...)]
And hence otherwise show that
P(X is odd ) :
1+q
Find P(X is odd|X < 3) as a function of q, and, given that
11](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe63f5d20-b31b-4b08-94f8-ed070ebd7c8d%2F31ceeee3-3466-41f4-b676-4d748d8f6ab6%2F28b4fyj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The random variable X has the geometric distribution with probability mass function (pmf)
Px (x) = q*p, x = 0, 1, 2, ... 0<p< 1,
where q = 1-p
i)
Find P(X > x) and show that P(X < 3) = 1-q*.
ii)
Explain why
P[X is odd(= 1,3,5,7, ...)] = q x P[X is even(= 0,2,4,6, ...)]
And hence otherwise show that
P(X is odd ) :
1+q
Find P(X is odd|X < 3) as a function of q, and, given that
11
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