5. (a) Suppose X is a discrete random variable with range in the positive integers {1, 2, 3, 4, . . .}. Show that PX(k) = FX(k) − FX(k − 1). (b) Suppose X is a discrete random variable with range in the increasing sequence of values {x1, x2, x3, . . .}, where x1 < x2 < x3 < · · · . Show that, for k ≥ 2, we have PX(xk) = FX(xk) − FX(xk−1). (c) Let X be the random variable in part (b), and suppose a < b are two values in the range of X. Show that P[a < X ≤ b] = FX(b) − FX(a).

5. (a) Suppose X is a discrete random variable with range in the positive integers {1, 2, 3, 4, . . .}. Show that PX(k) = FX(k) − FX(k − 1). (b) Suppose X is a discrete random variable with range in the increasing sequence of values {x1, x2, x3, . . .}, where x1 < x2 < x3 < · · · . Show that, for k ≥ 2, we have PX(xk) = FX(xk) − FX(xk−1). (c) Let X be the random variable in part (b), and suppose a < b are two values in the range of X. Show that P[a < X ≤ b] = FX(b) − FX(a).

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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