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Thread: Simple question on probability.

  1. #1
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    Simple question on probability.

    Alright... i am new to this forum...this may seems quite easy for you guys... but i've been very confused lately

    What is the maximum probability value that a cumulative density function (cdf) can have?

    Now i know that a probability can have a event of 0 to 1... asking for maximum probability i assume it will be 1? But then thinking again.. when it relates to CDF (which i don't fully understand) it can be limited to (.5) or even to infinite?

    So please guys.. any suggestions?
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  2. #2
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    Quote Originally Posted by holymackerel View Post
    Alright... i am new to this forum...this may seems quite easy for you guys... but i've been very confused lately

    What is the maximum probability value that a cumulative density function (cdf) can have?

    Now i know that a probability can have a event of 0 to 1... asking for maximum probability i assume it will be 1? But then thinking again.. when it relates to CDF (which i don't fully understand) it can be limited to (.5) or even to infinite?

    So please guys.. any suggestions?
    Do you understand that the cdf F(x) is an increasing function such that $\displaystyle \lim_{x \rightarrow +\infty} F(x) = 1$ .....?
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    let me give an example
    to be simple let consider a discret example
    F(x) is P(X<=x)
    like a F(5) is a sum i=0 to 5 of P(X=i) considering the X assumes values 0 to i infinte let's say

    so like u said the probability assumes values between 0 to 1 so the max of a F is the sum of all probabilites in all points and that's 1 by definition
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    so i was right that the max value is 1? i keep getting confuse with the CFD's parameters as it says x to infinite...

    which leads me to my next questions... that any random variable with a normal distribution can be converted to a random variable with a standard normal distribution? or am i wrong?

    and thanks for the prompt replies... you guys are great... helping an unknown fellow.. really appreciate it.
    Last edited by holymackerel; Apr 26th 2008 at 09:47 PM.
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    Quote Originally Posted by holymackerel View Post
    so i was right that the max value is 1? i keep getting confuse with the CFD's parameters as it says x to infinite...

    which leads me to my next questions... that any random variable with a normal distribution can be converted to a random variable with a standard normal distribution? or am i wrong?

    and thanks for the prompt replies... you guys are great... helping an unknown fellow.. really appreciate it.
    $\displaystyle Z = \frac{X - \mu}{\sigma}$

    where X ~ Normal($\displaystyle \mu, \, \sigma$) and Z ~ Normal (0, 1).
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    ok i was wrong... thanks =)
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    Quote Originally Posted by holymackerel View Post
    ok i was wrong... thanks =)
    No. You're right. I gave the conversion ......
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  8. #8
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    excellent, thanks again. i have to admit that probability is my weakest subject... as it's the most worded topic there is. i shall be back for further enquiries...
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