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…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 39E: Assume that the probability that an airplane engine will fail during a torture test is 12and that...

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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