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Math Help - need help with cdf homework

  1. #1
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    need help with cdf homework

    For each of the following functions, (1) find the constant, (2) find the c.d.f. F(x), (3) sketch graphs of f(x) and F(x) and (4) find mu and sigma squared.

    1. f(x) = x^2/3, 0 < x < c

    2. f(x) = (3/16) x^4; -c < x < c

    3. f(x) = 1/(cx)^(1/2), 0 < x < 1 (unbounded!)
    Last edited by mr fantastic; October 20th 2009 at 02:20 PM. Reason: Moved from original thread.
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  2. #2
    MHF Contributor matheagle's Avatar
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    To answer part 1. in each case, integrate and set that equal to ONE.
    Then solve for your c.
    Last edited by matheagle; October 20th 2009 at 03:48 PM. Reason: Clarified what part of the question this excellent advice applies to.
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  3. #3
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    Quote Originally Posted by affelix View Post
    For each of the following functions, (1) find the constant, (2) find the c.d.f. F(x), (3) sketch graphs of f(x) and F(x) and (4) find mu and sigma squared.

    1. f(x) = x^2/3, 0 < x < c

    2. f(x) = (3/16) x^4; -c < x < c

    3. f(x) = 1/(cx)^(1/2), 0 < x < 1 (unbounded!)
    Please show some effort here.

    Part 2 is found using the definition F(x) = \int_{-\infty}^x f(t) \, dt.

    Part 3 is basic graphing.

    Part 4 is done using the basic definitions E(X) = \int_{-\infty} ^{+\infty} x f(x) \, dx and Var(X) = E(X^2) - (E(X))^2 where E(X^2) = \int_{-\infty} ^{+\infty} x^2 f(x) \, dx (it's assumed that you know how to integrate).

    If you need more help then please show what you've done and where exactly you get stuck.
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