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Let X be a finite random variable on (N, F, P) (i.e., P(X = ∞) = P(X = -x) = 0). Show that its distribution function Fx satisfies the following properties: (a) Fx is non-decreasing.

Let X be a finite random variable on (N, F, P) (i.e., P(X = ∞) = P(X = -x) = 0). Show that its distribution function Fx satisfies the following properties: (a) Fx is non-decreasing.

A First Course in Probability (10th Edition)
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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Let \( X \) be a finite random variable on \((\Omega, \mathcal{F}, P)\) (i.e., \( P(X = \infty) = P(X = -\infty) = 0\)). Show that its distribution function \( F_X \) satisfies the following properties: (a) \( F_X \) is non-decreasing. (b) \( \lim_{x \to -\infty} F_X(x) = 0 \), and \( \lim_{x \to \infty} F_X(x) = 1 \).
Transcribed Image Text:Let \( X \) be a finite random variable on \((\Omega, \mathcal{F}, P)\) (i.e., \( P(X = \infty) = P(X = -\infty) = 0\)). Show that its distribution function \( F_X \) satisfies the following properties: (a) \( F_X \) is non-decreasing. (b) \( \lim_{x \to -\infty} F_X(x) = 0 \), and \( \lim_{x \to \infty} F_X(x) = 1 \).
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