Results 1 to 7 of 7

Math Help - Exponential random variable

  1. #1
    Member
    Joined
    Mar 2010
    Posts
    122

    Exponential random variable

    Let T be an exponential random variable with parameter lamba.Compute E[T/T<=t]
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member Sambit's Avatar
    Joined
    Oct 2010
    Posts
    355
    In case you don't know the general form of computing such an expectation, follow THIS link.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Mar 2010
    Posts
    122
    Thanks for the link but I was looking for someone to show me the steps and explain how the expectation is affected because of the conditioning.
    Last edited by CaptainBlack; March 19th 2011 at 02:22 AM. Reason: Remove insulting tone
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by ulysses123 View Post
    Thanks for the link but was looking for someone to show me the steps and explain how the expectation is affected because of the conditioning.
    p(T|T<t)=p(T)/p(T<t) for T<t and zero otherwise

    CB
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Senior Member Sambit's Avatar
    Joined
    Oct 2010
    Posts
    355
    Quote Originally Posted by CaptainBlack View Post
    p(T|T<t)=p(T)/p(T<t) for T<t and zero otherwise

    CB
    This is supposed to help you perfectly. Just multiply the values with corresponding probabilities and integrate over zero to infinity.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Mar 2010
    Posts
    122
    Thanks for your reply captain black. I thought that P(T/T<=t) will become
    P(T) because the fact that the waiting time was <t has no effect on the distribution of the time you will wait due to the memorylessness property, but you have P(T/T<=t)=P(T,T<=t)/P(T<=t) written as P(T)/P(T<t).
    I know you are most likely correct, but i would like to understand the logic as i am not getting how you arrived at this.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by ulysses123 View Post
    Thanks for your reply captain black. I thought that P(T/T<=t) will become
    P(T) because the fact that the waiting time was <t has no effect on the distribution of the time you will wait due to the memorylessness property, but you have P(T/T<=t)=P(T,T<=t)/P(T<=t) written as P(T)/P(T<t).
    I know you are most likely correct, but i would like to understand the logic as i am not getting how you arrived at this.
    Put the expression for the density and p(T<t) into the expression and you will see that the given expression for p(T|T<t) has the required memoryless property.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Exponential random variable: prove μ=σ
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: October 21st 2010, 06:32 PM
  2. Expectation of exponential random variable.
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: August 24th 2010, 04:03 AM
  3. Independent Random Variable (exponential function)
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: April 27th 2010, 05:09 PM
  4. exponential random variable with a random mean?
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: March 21st 2010, 03:05 PM
  5. exponential random variable
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: May 17th 2009, 07:54 AM

Search Tags


/mathhelpforum @mathhelpforum