Results 1 to 2 of 2

Math Help - probability calculation and marginal pdf

  1. #1
    Member
    Joined
    Jul 2010
    Posts
    99

    probability calculation and marginal pdf

    Two people plan to meet to go to the bar. Each of them arrives at a time uniformly distributed between midnight and 1am and independently of the other. Denote X (respectively Y) the random variable representing the arrival time of the first person (respectively, the second). The joint probability distribution is given by:
    f_{(X,Y)}{(x,y)}=\left\{\begin{array}{cc}2,&\mbox{  if}\ 0\leq x\leq y\\0, &\mbox{otherwise}\end{array}\right.

    (a)Find the probability that the first person is waiting for his friend for more than 10 minutes.

    (b)Determine the marginal probability density functions of X and Y. Check that thery are indeed probability density functions.


    What I did so far is P(x>10)=1-P(x\leq10)
    Then I use formula F_{X}{(x)}=\int_{0}^{x} f(y) dy
    And the formula f_{Y}{(y)}=\int_{-\infty}^{\infty}f_{(X,Y)}{(x,y)}dx
    But I end up F_{X}{(x)}=x^2, there for, the probability is no longer less than 1.

    I really don't know what to do now, I thought I got the right formulae, can anyone help me please. It is same for part (b), I kind of get something, use formulae, but as question required, when I check my answer, I realised the integration of density functions don't give me 1, which means I must be wrong.

    Please help me. Thanks a lot.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Mar 2011
    Posts
    2
    Hint: Question is given in hours, not minutes. So x<1/6, etc. You don't need the marginals for A.

    For b, use the bounds on y when integrating wrt y, not the bounds on x (e.g. y goes from x to 1), and the f_{Y}{(y)}=\int_{-\infty}^{\infty}f_{(X,Y)}{(x,y)}dx can be used for both marginals.
    Last edited by Aylix; May 3rd 2011 at 07:52 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Joint Probability/Marginal Probability
    Posted in the Statistics Forum
    Replies: 0
    Last Post: March 2nd 2010, 10:15 PM
  2. Replies: 1
    Last Post: February 18th 2010, 01:54 AM
  3. Marginal Probability Mass Function
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: November 12th 2009, 09:03 PM
  4. Marginal Probability
    Posted in the Statistics Forum
    Replies: 2
    Last Post: June 15th 2009, 04:36 AM
  5. marginal probability density function
    Posted in the Advanced Statistics Forum
    Replies: 7
    Last Post: March 17th 2009, 12:04 PM

Search Tags


/mathhelpforum @mathhelpforum