Results 1 to 2 of 2

Math Help - just a little help with random variables

  1. #1
    Newbie
    Joined
    Nov 2006
    Posts
    9

    just a little help with random variables

    I can't figure this out. Help appreciated.

    A box contains four balls, numbered 1 through 4. One ball is selected at random from this box.
    Let X1=1 if ball number 1 or ball number 2 is drawn.
    Let X2=1 if ball number 1 or ball number 3 is drawn.
    Let X3=1 if ball number 1 or ball number 4 is drawn.
    The Xi values are zero otherwise. Show that any two of the random variables X1, X2, X3 are independent but that the three together are not.

    I could really use some help. Thank you.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Mar 2006
    Posts
    125
    what you have to do is to define the probabilities of all the events:

    P(X1) = 1/2 , because X1 will occur ( be 1 ) when the ball will have numbers 1 or 3 out of 4 options, meaning 2/4.
    in the same way:
    P(X2)=1/2
    P(X3)=1/2

    now you have to look at the intersections:

    P(X1 and X2 ) = 1/4 (why ? ), and also P(X1)*P(X2)=1/4, so X1 and X2 are independent.
    do the same for X1 & X3, X2 & X3.

    the probability of all Xi to occur is 1/4, while P(X1)*P(X2)*P(X3)=1/8, so all the events are not independent.
    you say that the 3 events are pairwise independent.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: June 5th 2011, 04:57 PM
  2. Random Variables
    Posted in the Advanced Statistics Forum
    Replies: 6
    Last Post: April 9th 2010, 08:49 PM
  3. Replies: 3
    Last Post: January 13th 2010, 11:44 AM
  4. random variables
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: January 23rd 2009, 05:26 AM
  5. Random Variables
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: October 28th 2008, 05:51 PM

Search Tags


/mathhelpforum @mathhelpforum