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November 14th, 2015, 12:19 AM   #1
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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.
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November 14th, 2015, 05:29 AM   #2
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Quote:
Originally Posted by mhhojati View Post
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 $\displaystyle P(T\ge t)= \int_t^{\infty} f_T(t')dt'$
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November 14th, 2015, 05:48 AM   #3
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Originally Posted by Country Boy View Post
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
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