Banner Ad 1

Collapse

Announcement

Collapse
No announcement yet.

max(x,y) question

Collapse
This topic is closed.
X
X
 
  • Filter
  • Time
  • Show
Clear All
new posts

  • max(x,y) question

    Suppose X~U(0,4), and Y ~exp(2) are independent.

    Calculate P(max(X,Y)<2/3 | X<2)

    I am having difficultites with these types of questions. Could someone illustrate the solution?

    Thank you

  • #2
    F(max(x,y))=P(Both X and Y<=2/3)=Fx(2/3)Fy(2/3) <----Independence. The rest should be trivial.

    For order statistics you generally start with the distribution. To find the density you need to differentiate the distribution.

    You do have a textbook don't you?

    Comment


    • #3
      Originally posted by managuense
      F(max(x,y))=P(Both X and Y<=2/3)=Fx(2/3)Fy(2/3) <----Independence. The rest should be trivial.

      For order statistics you generally start with the distribution. To find the density you need to differentiate the distribution.

      You do have a textbook don't you?
      managuense's formula looks right, except you have to account for X<2 as a given. That should be Fx(2/3 | X<2) * Fy(2/3).

      Comment

      Working...
      X