Products
Rewards 
from HOLOOLY

We are determined to provide the latest solutions related to all subjects FREE of charge!

Please sign up to our reward program to support us in return and take advantage of the incredible listed offers.

Enjoy Limited offers, deals & Discounts by signing up to Holooly Rewards Program

HOLOOLY 
BUSINESS MANAGER

Advertise your business, and reach millions of students around the world.

HOLOOLY 
TABLES

All the data tables that you may search for.

HOLOOLY 
ARABIA

For Arabic Users, find a teacher/tutor in your City or country in the Middle East.

HOLOOLY 
TEXTBOOKS

Find the Source, Textbook, Solution Manual that you are looking for in 1 click.

HOLOOLY 
HELP DESK

Need Help? We got you covered.

Chapter 2

Q. 2.3

Let the random variable X represent the DC voltage output from some force transducer, and let the distribution be uniform on the set [-4,16] such that F_{X}(u)=0.05 (u+4) for -4 \leq u \leq 16. Of course, F_{X}(u)  is zero to the left and unity to the right of the [-4,16] interval. Now let another (mixed) random variable Y represent the output from a voltmeter that reads only from zero to 10 volts and that has X as the input. Whenever 0 \leq X \leq 10 we will have Y = X, but we will get Y=0 whenever X \lt 0, and Y=10 whenever X \gt 10. Find the cumulative distribution function for Y.

Step-by-Step

Verified Solution

From P(Y \leq u) we get

F_{Y}(u)=0 For u \lt 0
F_{Y}(u)=0.05(u+4) For 0 \leq u \lt 10
F_{X}(u)=1 For u \geq 10

This F_{Y}(u) function for this mixed random variable has discontinuities of 0.2 at u=0 and 0.3 at u=10, representing the finite probabilities that Y takes on these two particular values.