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Math Help - Cumulative Distribution function

  1. #1
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    Cumulative Distribution function

    Lets say I have a random variable X that can take values 1,2,3,4 and 5 with probabilities 0.2 0.3 0.1 0.25 0.10 0.05.

    My question is how I can determine the Cumulative distribution function and how I can use it to generate the numbers from X?
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  2. #2
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    You have five values and six probabilities.
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  3. #3
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    Quote Originally Posted by stordase39 View Post
    Lets say I have a random variable X that can take values 1,2,3,4 and 5 with probabilities 0.2 0.3 0.1 0.25 0.10 0.05.

    My question is how I can determine the Cumulative distribution function?
    I will get you started on the CDF:
    \[<br />
P\left( {X \leqslant b} \right) = F(b) = \left\{ {\begin{array}{rl}<br />
   {0,} & {b < 1}  \\<br />
   {0.2,} & {1 \leqslant b < 2}  \\<br />
   {0.5,} & {2 \leqslant b < 3}  \\<br />
   {?,} & {3 \leqslant b < 4}  \\<br />
   ?, & ?  \\<br />
   ?, & ?  \\ \end{array} } \right.
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  4. #4
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    Ok sorry for that... say that the probabilities are 0.2 0.3 0.1 0.1 0.3 then. How can i generate numbers from that distribution using the CDF.
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  5. #5
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    Quote Originally Posted by stordase39 View Post
    Ok sorry for that... say that the probabilities are 0.2 0.3 0.1 0.1 0.3 then. How can i generate numbers from that distribution using the CDF.
    Read post #3. Learn from it. Post all your work and say where you get stuck.
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    Quote Originally Posted by mr fantastic View Post
    Read post #3. Learn from it. Post all your work and say where you get stuck.
    I know how to contruct the CDF now. My question is how to generate numbers from the distribution using the CDF?
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  7. #7
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    Quote Originally Posted by stordase39 View Post
    I know how to contruct the CDF now. My question is how to generate numbers from the distribution using the CDF?
    What do you mean by that question?
    What numbers?
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  8. #8
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    Quote Originally Posted by Plato View Post
    What do you mean by that question?
    What numbers?
    I'm inclined to suggest to the OP that s/he make a spinner, with the area for each number weighted according to the probability of that number occuring.

    Memo to OP: The usefulness of the help you get is directly proportional to the accuracy and clarity of the question you post.
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  9. #9
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    Quote Originally Posted by Plato View Post
    What do you mean by that question?
    What numbers?
    I think what he means is: Given a RV X \sim U(0,1) find a transformation f(.) such that Y=f(X) has the required distribution?

    The answer required is then:

    y=F^{-1}(x)


    CB
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