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i) Find P(X 2 x) and show that P(X < 3) = 1-q*. i) 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 ) =a ii) Find P(X is odd|X < 3) as a function of q. and, given that

i) Find P(X 2 x) and show that P(X < 3) = 1-q*. i) 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 ) =a ii) Find P(X is odd|X < 3) as a function of q. and, given that

Algebra & Trigonometry with Analytic Geometry
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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|A5 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 2 x) and show that P(X < 3) =1 – q*. ii) Explain why P[X is odd(= 1,3,5,7, ...] = q × P[X is even(= 0,2,4,6, ..)] And hence otherwise show that P(X is odd ) = 1+9 iii) Find P(X is odd|x < 3) as a function of q, and, given that
Transcribed Image Text:|A5 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 2 x) and show that P(X < 3) =1 – q*. ii) Explain why P[X is odd(= 1,3,5,7, ...] = q × P[X is even(= 0,2,4,6, ..)] And hence otherwise show that P(X is odd ) = 1+9 iii) Find P(X is odd|x < 3) as a function of q, and, given that
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