Answered: [10] Let X be a continuous RV with CDF…

[10] Let X be a continuous RV with CDF 0, x<-2 Fx (x) =+ (4x-2), +2(4x), -2≤x<2. 1, (a) Find P(X < 0), P(-1 < x < 1) and P(0.5

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.3: Systems Of Inequalities

Problem 19E

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Question

Let X be a continuous RV with CDF

Find P(X < 0), P(-1 < X < 1) and P(0.5 < X).

Based on your answers to the above questions, what is the median of the distribu-tion? Why

Find the PDF, fx (x), of X.

[10] Let X be a continuous RV with CDF
0,
x<-2
Fx (x) =+ (4x-2),
+2(4x), -2≤x<2.
1,
(a) Find P(X < 0), P(-1 < x < 1) and P(0.5 <X).
2≤x
(b) Based on your answers to the above questions, what is the median of the distribu-
tion? Why?
(c) Find the PDF, fx(x), of X.

Definition Definition Probability of occurrence of a continuous random variable within a specified range. When the value of a random variable, Y, is evaluated at a point Y=y, then the probability distribution function gives the probability that Y will take a value less than or equal to y. The probability distribution function formula for random Variable Y following the normal distribution is: F(y) = P (Y ≤ y) The value of probability distribution function for random variable lies between 0 and 1.

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