DSE 2010

[poonam]

Please let me know the way to solve such a question as follows..
Suppose X1,............Xn are observed completion times of an experiment with values in [0,1]. Each of these random variables is uniformly distributed on[0,1]. If Y is the maximum observed completion time, then the mean of Y is ??

[priyanka]

solution is provided in solved problems in lessons refer that

[poonam]

Pr(Y >= y) = Pr(X1>=y, X2>=y........Xn>=y)
               = Pr(X1 >= y)
. Pr(X2>=  y)
.............
Pr(Xn>=y)    by independence of Xi's
               = y^n

Above is a part of the solution, I would love it if you could let me know, how did we get the probability ="y^n"
The first two steps are fine... just the last one.

Thank you..

[Amit Goyal]

First of all this is not what is posted in the solution. I guess you read it wrong. The solution had Pr(Y<=y) not Pr(Y>=y). If this why you are not getting it. You may try it again. If you still can't get it then you need to revise uniform distribution.

[poonam]

I got it !! thanks !! :-)