If Xi , i = 1, 2, 3, are independent exponential random variables with rate lambda_i, i=1, 2, 3 find E[max Xi \ X1<X2<X3] ,
How can I proof that the answer is (1/lambda1+lambda2+lambda3)+(1/lambda2+lambda3)+(1/lambda3)
If Xi , i = 1, 2, 3, are independent exponential random variables with rate lambda_i, i=1, 2, 3 find E[max Xi \ X1<X2<X3] ,
How can I proof that the answer is (1/lambda1+lambda2+lambda3)+(1/lambda2+lambda3)+(1/lambda3)
From what you've written I think you want the expected value of the largest order statistic
from a sample of size three from an exponential distribution.
If that's true, you should find the density of that order stat then integrate.
Nope, I was wrong. Your random variables have different parameters.
But you can still derive the density of the largest of these three.