Hi Guy's
I was wondering if anyone can check my work to see if I'm on the right track.

I was given the question

The random variable X has density f(x)= 1/2 e^(-x/2) for x>0


Find a number x0 such that P(X > x0) = 1/2


What I did was find the integral of f(x)= 1/2 e^(-x/2)
which equals

-e^(-x/2)

and solved for x

-e^(-x/2) = 1/2

x = 1.386

so I integrate

1/2 e^(-x/2) between [1.386, infinity] which gives 1/2

Is this right?

regards
Brendan