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Math Help - Cumulative distribution function probs

  1. #1
    Junior Member plm2e's Avatar
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    Cumulative distribution function probs

    Let random variable X have the cdf F given by:

    F(x)= { 0 for x ≤ 0
    (x^3/8) for 0< x<2
    1 for x ≥ 2


    1. Find P(X ≤ 2/3)

    [(2/3)^3]/8 = .37



    2. Find the probability density function for X

    f(x) = x^2/16


    3. Let random Variable Y = F(X). Find the Probability P(Y ≤ 2/3)



    I just want to check my answers for parts 1 and 2. Can someone please help me with part 3
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  2. #2
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    mr fantastic's Avatar
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    Quote Originally Posted by plm2e View Post
    Let random variable X have the cdf F given by:

    F(x)= { 0 for x ≤ 0
    (x^3/8) for 0< x<2
    1 for x ≥ 2


    1. Find P(X ≤ 2/3)

    [(2/3)^3]/8 = .37



    2. Find the probability density function for X

    f(x) = x^2/16


    3. Let random Variable Y = F(X). Find the Probability P(Y ≤ 2/3)



    I just want to check my answers for parts 1 and 2. Can someone please help me with part 3
    1. [(2/3)^3]/8: Correct. 0.37: Wrong.

    2. f(x) = dF/dx. You have not differentiated correctly.
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