D5 2 Let X be a discrete random variable with PMFPx(x) = ca²x, x=1,2,...where 0 < a < 1.+∞(a) Write down an expression for a²n, for |a| < 1.n=0(b) Obtain c, identify the distribution of X and deduce E[X] and var(X).

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Answered: Let X be a discrete random variable…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 22E

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Let X be a discrete random variable with PMF Px(x)=ca²ª, x=1,2,... where 0 < a < 1. (a) Write down an expression for Σa²¹, for |a| < 1. n=0 (b) Obtain c, identify the distribution of X and deduce E[X] and var(X). +∞o