Let a random variable X has the following function: FX(x) = { 0 ; x < 0 (1/2)+(x/2) ; 0 ≤ x < 1 1 ; x ≥ 1. Verify that FX(x) is a CDF. Determine (i) the PDF of X, (ii) E[e^X], (iii) P[X = 0|X≤ 0.5].

Let a random variable X has the following function: FX(x) = { 0 ; x < 0 (1/2)+(x/2) ; 0 ≤ x < 1 1 ; x ≥ 1. Verify that FX(x) is a CDF. Determine (i) the PDF of X, (ii) E[e^X], (iii) P[X = 0|X≤ 0.5].

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.2: Exponential Functions

Problem 31E

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Question

Let a random variable X has the following function:
FX(x) = {

0 ; x < 0
(1/2)+(x/2) ; 0 ≤ x < 1
1 ; x ≥ 1.

Verify that FX(x) is a CDF. Determine (i) the PDF of X, (ii) E[e^X], (iii) P[X = 0|X≤ 0.5].

Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.

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