can not understand the probablity problem, pls HELP! Urgent

From: bin (binye1973_at_yahoo.com)
Date: 11/18/04 

Date: Wed, 17 Nov 2004 18:11:04 -0600

Consider a particular Ph.D. student; we know that after she begins her Ph.D.
program, the number of years it takes her to complete her studies is a
random
variable with distribution exp(1/4) (independent of when she started).
Suppose
you know that the student completed her Ph.D. today. We wish to estimate how
long ago she started. Assume that the a priori distribution of X is uniform
on
[3, 6].
a. Let X represent the number of years ago the student started. Let Y
represent the observation of when she completes, relative to today (so the
given observation is Y = 0).
Find fY | X(y | x)
for x >= 0.

can not understand the meaning very precisely ,which is X , which is Y, what
is realation between the exp(1/4) and uniform of [3,6].

 thanks

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