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Math Help - Cumulative Distribution Functions

  1. #1
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    Cumulative Distribution Functions

    I cant remember anything about CDF's Please can someone help with this question!!!

    Obtain the cumulative distribution function of the following discrete random variables
    (A) Bin(3 , theta)
    (B) Unif( 0 , m)
    (C) Geom( Theta )

    The question did give hints but they don't help me what so ever

    HINT
    First calculate F at the integers. (Distinguish the index of the summation from the upper limit of summation). Secondy extend from the integers to the real line.

    Any help would be appreciated!!!
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  2. #2
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    Re: Cumulative Distribution Functions

    Hey Matt1993.

    Hint: For discrete distributions P(X <= x) = Sigma (i = 0 to x) P(X = x) [Assuming that the first event is X = 0]. For continuous distributions, P(X < x) = Integral [-infinity,x] f(u)du. These are standard definitions.

    Given the above, what is P(X = x) for (a) and (c) and what is f(u) for b?
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  3. #3
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    Re: Cumulative Distribution Functions

    Ok so
    For bin(3, Theta) then p(r) = (nCr)*(theta)^(r)*(1- theta)^(n-r)
    For unif(0, m) then p(r) = 1/(m+1) for r = 0,1,2,3,...,m or 0 otherwise
    For geom p(r) = (1- theta)^r * theta for 0,1,2,3,....
    Were would I go from here thanks for this
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  4. #4
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    Re: Cumulative Distribution Functions

    For the discrete you need to sum all values greater than or equal to a particular value in terms of probabilities.

    So for Binomial (and other discrete) you have P(X <= 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3).

    For uniform you have P(X < x) = Integral [0,x) f(u)du = Integral [0,x) 1*du.

    Remember that for discrete you add up all individual cases that satisfy the inequality and for continuous you use the integral definition I provided above.
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