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don't understand jointly continous distributions

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  • don't understand jointly continous distributions

    What I don't understand is how to come up with limits of integration. I know how to integrate. Like say if you have a basic question like:

    Let R be the region in the 1st quadrant bounded by the curves y=x and y=x^5. A random point (X,Y) is selected from R.

    Calculate the marginal PDF of X and Y. From the interval 0 to 1.


    The answers are (1/.3333)(x-x^5)
    and (1/.3333)(-y+y^1/5)

    What I tried to do was start by graphing the problem. Easily seeing the that they intersect at x=0 and x=1.

    So in setting up the integrals I come to a dillema. I'm pretty sure that one of them will be from 0 to 1, but the other I don't know. Is it from 0 to y or 0 to x. I am confused and frustrated about this concept. I know it's probably real simple. It just isn't clicking in me yet.
    Please help me.

  • #2
    From x^5 to x, and from y to y^(1/5)


    • #3
      If you integrate first with respect to y, it goes from x^5 to x, and x goes 0 to 1. If you go first with respect to x, it goes from y to y^(1/5) and y goes from 0 to 1.