The Difference of Two Independent Exponential Random Variables

MIT 6.041SC Probabilistic Systems Analysis and Applied Probability, Fall 2013
View the complete course: ocw.mit.edu/6-041SCF13
Instructor: Kuang Xu
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
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[@plrc4593]

Thanks dude! That helped me to figure out what if X and Y are exponential random variables with different parameters.

[@milosnovakovic3942]

If, lets say, X ~ EXP(LAMBDA1 = L1) and Y~ EXP(LAMBDA2 = L2), then we have for Z = Y - X, that pdf of Z is
...............{ (L1*L2/(L1+L2)) * e^(-L1*z), when z>=0
f_Z (z) = {
...............{ (L1*L2/(L1+L2)) * e^(L2*z), when z

[@lahaale5840]

Hi, should we add a condition that lambda > 0? otherwise there is an issue on the last step integral, right? when lambda

[@charlesreed8420]

how would you do this when the two random variables at the start have different parameters? e.g: X~Exp(a), Y~Exp(b)

[@chybaty21]

i don't see how to examine z0, what does it change?

[@aniketsaha7455]

It simply means that who came first...Romeo or Juliet...now in first case the expression is exp(lamda*z)...lamda has to be positive(for exponential distribution) so z =0 we see that distribution is exp(-lamda*z) with again lamda >0...so that our distribution again converges on right side...

[@cengizhancengiz211]

dont you need examine z>0 ? tehere should be 2 case ı think!

[@lahaale5840]

he had checked z >=0