# Thread: demonstration with discrete random variable

1. ## demonstration with discrete random variable

I would like to know if anybody from this forum have some insights about how to handle this demonstration:

"Show that for any discrete random variable X, etE[X] <= E[etX], where t is fixed and belongs to R." (E is expected value)

Maybe this is related with Jansen inequality, but certainly I'm not good regarding demonstrations.

By the way how can I learn the way of posting formulas in the forum?

Regards.

2. ## Re: demonstration with discrete random variable

Originally Posted by rbriceno
I would like to know if anybody from this forum have some insights about how to handle this demonstration:
"Show that for any discrete random variable X, etE[X] <= E[etX], where t is fixed and belongs to R." (E is expected value)
Maybe this is related with Jansen inequality, but certainly I'm not good regarding demonstrations.
By the way how can I learn the way of posting formulas in the forum?
You must learn to code in LaTeX.

\$e^{\mathcal{E}[tX]}\$ gives $e^{\mathcal{E}[tX]}$

\${\mathcal{E}[e^{tX}]}\$ gives $\mathcal{E}[e^{tX}]$