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. 2.2

Let X denote a real number chosen “at random” from the interval [0,10]. Find the cumulative distribution function of X.

Step-by-Step

Verified Solution

In this case there is a continuous set of possible values for the random variable, so there are infinitely many values that the random variable X might assume and it is equally likely that X will take on any one of these values. Obviously, this requires that the probability of X being equal to any particular one of the possible values must be zero, because the total probability assigned to the set of all possible values is always unity for any random variable (Axiom 2 of probability theory, also called total probability). Thus, it is not possible to define the probabilities of this random variable by giving the probability of events of the type {X=u}, but there is no difficulty in using the cumulative distribution function. It is given by

F_{X}(u)=0 For -\infty \lt u \lt 0
F_{X}(u)=0.1u For 0 \leq u \lt 10
F_{X}(u)=u For 10 \leq u \lt \infty

For example, P(0 \leq X \leq 4) = F_{X}(4) – F_{X}(0) =0.4.