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Math Help - 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 \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; April 26th 2008 at 10:47 PM.
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  5. #5
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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.
    Z = \frac{X - \mu}{\sigma}

    where X ~ Normal( \mu, \, \sigma) and Z ~ Normal (0, 1).
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    ok i was wrong... thanks =)
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  7. #7
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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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