My Math Forum Help in understanding the CDF

 Probability and Statistics Basic Probability and Statistics Math Forum

 November 14th, 2015, 12:19 AM #1 Member   Joined: Jan 2012 Posts: 57 Thanks: 0 Help in understanding the CDF The CDF of a continuous random variable X is defined as: but in situation like this I usually encounter with such CDF function which I do not understand how one came up with What is wrong with the following equiton? $\displaystyle F_{T}(t)=P(T\leqslant t )=\int_{0}^{t}f_{T}(t')dt'=1-P(T\geq t )$ Last edited by mhhojati; November 14th, 2015 at 12:22 AM.
November 14th, 2015, 05:29 AM   #2
Math Team

Joined: Jan 2015
From: Alabama

Posts: 3,198
Thanks: 872

Quote:
 Originally Posted by mhhojati The CDF of a continuous random variable X is defined as: but in situation like this I usually encounter with such CDF function which I do not understand how one came up with
You don't get that! Where did you see it?
The correct statement is that $\displaystyle P(T\le t)= \int_0^t f_T(t')dt'$.
That is, "$\displaystyle \le$", not "$\displaystyle \ge$".

Quote:
 What is wrong with the following equiton? $\displaystyle F_{T}(t)=P(T\leqslant t )=\int_{0}^{t}f_{T}(t')dt'=1-P(T\geq t )$
Nothing is wrong with it. That is the correct formula. You could also write it as $\displaystyle P(T\ge t)= \int_t^{\infty} f_T(t')dt'$

November 14th, 2015, 05:48 AM   #3
Member

Joined: Jan 2012

Posts: 57
Thanks: 0

Quote:
 Originally Posted by Country Boy You don't get that! Where did you see it?
it was given in the solution manual problem 10.5.6 from Problem Solutions July 26, 2004 Draft
Roy D. Yates and David J. Goodman

 Tags cdf, understanding

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post math123321 Algebra 1 November 5th, 2015 04:26 PM erpi Calculus 1 August 17th, 2014 01:24 PM dawgphysics Applied Math 1 June 26th, 2014 07:32 AM SamSeymour Pre-Calculus 2 April 3rd, 2014 11:28 AM RealMadrid Calculus 2 July 26th, 2012 08:16 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top