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Probability: Cumulative distribution problem

  1. Nov 25, 2012 #1
    1. The problem statement, all variables and given/known data

    Example 5.1.4: Y is a continuous random variable on the interval (0; 1) with
    density function
    fY (y) =
    {3y2 0 < y < 1
    {0 elsewhere
    what is the cumulative distribution function of Y ?

    2. Relevant equations

    The relationship between a continuous random variable and the cumulative distribution function can be defined as: F(a) = P{X ∈ (-∞,α)} = ∫(-∞,α) f(x)dx

    3. The attempt at a solution

    Is the problem just asking for this: P{Y ∈ (0,1)} ?

    In terms of the integration, the indefinite integral is y^3 + C.

    Alas i am stuck!
     
  2. jcsd
  3. Nov 25, 2012 #2

    Ray Vickson

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    You wrote F(a) = ∫(-∞,α) f(x)dx. So, what is f(x) for x < 0? Can you replace the lower limit (-∞) by something else when a > 0? In other words, can you say
    [tex] F(a) = \int_{\text{something}}^a f(x) \, dx,[/tex] with 'something' ≠ -∞?

    And NO: the problem is not asking you for P{Y ∈ (0,1)}; it is asking you for the cumulative distribution function (which you have already defined!).

    RGV
     
    Last edited: Nov 25, 2012
  4. Nov 25, 2012 #3
    You mean this:

    [tex] F(a) = \int_{\text{0}}^1 y^3 \, dx,[/tex]
     
  5. Nov 26, 2012 #4
    Edit:

    [tex] F(a) = \int_{\text{0}}^1 3y^2 \, dy,[/tex]

    Sorry, i previously responded via phone.
     
  6. Nov 27, 2012 #5

    haruspex

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    The RHS is not a function of a.
     
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