# P(X>x)=e^-ax, x less/equal 0

1. Nov 5, 2009

Let X be a continuous random variable with

P(X>x)=e^-ax, x less/equal 0

Where a is a positive constant. Find EX and Var(x)

2. Nov 5, 2009

### HallsofIvy

Staff Emeritus
If P(X> x)= e^{-ax}, x less than or equal to 0, then the probability density function is p(x)= -a e^{-ax}.

Now just use the definitions:
$$E(x)= -a \int_x^0 xe^{-ax}dx[/itex] and [tex]Var(x)= -a \int_x^0 (x- E(x))^2e^{-ax}dx= -aE(x)\int_x^0 x^2e^{-ax}- E^2(x)$$