i hope you can help , please help , probability question?

Question

Let A be a random variable with the Exponential(1) distribution.
Let B be a random variable with the Uniform[0,1] distribution.
i) Show that for x,y > 0, the conditional probability that A > x+y given that A > x is
equal to the probability that A > y. This is called the memoryless property of the
exponential distribution; can you see why?
ii) Show that for 0 < x < 1, 0 < y < 1, the conditional probability that B > x+y given
that B > x is strictly less than the probability that B > y.

Answer 1

Maybe I can help. I remember doing i

Use the definition of conditional probability and do the integrals:

P(A>x+y | A>x ) = P(A>x+y and A>x)/P(A>x), right?

Try working out the integrals.