Turn on thread page Beta
    • Thread Starter
    Offline

    20
    ReputationRep:
    The book I'm using defines the CDF, F as:

    F = P(U<V) where U is the random variable being mapped onto the sample space, V.

    Yet online, and in fact in most sources, the CDF is defined as:

    F = P(U≤V).

    When we want to find the probability of an interval in the given sample space, say P(C), the two give slightly different answers:

    P(C) = P(U<V2) - P(U<V1) = P(V1 ≤ U < V2)
    or
    P(C) = P(U<V2) - P(U<V1) = P(V1 < U ≤ V2)

    I don't understand how two slightly different definitions can supposedly give the same answer. Can anyone expand on this and explain if they are the same or they aren't and also why?
    Offline

    14
    ReputationRep:
    (Original post by djpailo)
    The book I'm using defines the CDF, F as:

    F = P(U<V) where U is the random variable being mapped onto the sample space, V.

    Yet online, and in fact in most sources, the CDF is defined as:

    F = P(U≤V).
    The less-than-or-equals definition is the standard one. A typo in your textbook?
    • Thread Starter
    Offline

    20
    ReputationRep:
    (Original post by Gregorius)
    The less-than-or-equals definition is the standard one. A typo in your textbook?
    Can't be a typo because it is used throughout the book
    Offline

    14
    ReputationRep:
    (Original post by djpailo)
    Can't be a typo because it is used throughout the book
    A quick look around finds wikipedia saying that the  \le convention is "not universally used" and that there are problems with the alternative (in the use of discrete distributions, for example). It identifies the Hungarian mathematical literature as using  &lt; .
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: March 16, 2016

University open days

  1. University of Bradford
    University-wide Postgraduate
    Wed, 25 Jul '18
  2. University of Buckingham
    Psychology Taster Tutorial Undergraduate
    Wed, 25 Jul '18
  3. Bournemouth University
    Clearing Campus Visit Undergraduate
    Wed, 1 Aug '18
Poll
How are you feeling in the run-up to Results Day 2018?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.