Results 1 to 3 of 3

Math Help - Actuarial Science help: Survival Models

  1. #1
    Newbie
    Joined
    Jan 2010
    Posts
    2

    Actuarial Science help: Survival Models

    Could somebody please help me with the following problems:

    Let X1 and X2 be independent random variables. Define the variables Y =min(X1,X2) and Z = max(X1,X2).
    a) Show that Sy(y) is the product of the survival distribution functions of X1 and X2.
    b) Show that Fz(z) is the cumulative distribution functions of X1 and X2.
    c)Show that if X1 and X2 both have exponential distributions, then Y also has an exponential distribution, but Z does not.
    .................................................. ..............

    Let the independent random variables X1 and X2 both have exponential distributions, with parameters lambda1 and lambda2 respectively, where lambda1>lambda2. Let Y =min(X1,X2) and Z =max(X1,X2). Given that
    Sy(2) = 0.24 and Sz(2) = 0.86, find the value of lambda1.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    First of all, I do not use this S function.
    So I had to guess it was 1-F.

    S_Y(y)=P(Y>y) =P(X_1>y, X_2>y) =P(X_1>y)P(X_2>y)= S_{X_1}(y)S_{X_2}(y)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jan 2010
    Posts
    2
    Thank you for your help. Your explanation helped me figure out how to do the rest of the problems as well.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Survival Table
    Posted in the Math Software Forum
    Replies: 0
    Last Post: December 9th 2009, 11:32 AM
  2. Help with Actuarial Science Problem
    Posted in the Advanced Math Topics Forum
    Replies: 0
    Last Post: October 24th 2009, 06:59 AM
  3. Survival Analysis
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: August 1st 2009, 12:57 AM
  4. survival function
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: May 3rd 2009, 08:43 PM
  5. Replies: 2
    Last Post: July 17th 2007, 05:11 AM

Search Tags


/mathhelpforum @mathhelpforum