Thread: Expectation of an exponential

Hi all,

I'm new here - was hoping for some help with a simple (?) problem.

If 'x' is a uniform random variable with mean 'y' (i.e. y = <x>) and 'a' is a constant, what is <exp(-a*x)>?

Can this quantity be related to <x>?

David

Originally Posted by dcuccia

Hi all,

I'm new here - was hoping for some help with a simple (?) problem.

If 'x' is a uniform random variable with mean 'y' (i.e. y = <x>) and 'a' is a constant, what is <exp(-a*x)>?

Can this quantity be related to <x>?

David

$\displaystyle <g(X)> = \int_{- \infty}^{+ \infty} g(x) \cdot f(x) \, dx$ where f(x) is the pdf of X.

Thanks!

I've also learned that the particular case I was considering ( exp(-a*<x>) greater than <exp(-a*x)>) falls into a larger set of relations referred to as Jensen's Inequality.

Lots to learn...can't believe I never grok'd this as a Physics major.

Cheers,
David