# Continuous random variable with a probability density function

• Sep 3rd 2010, 09:40 PM
Supernova
Continuous random variable with a probability density function
A continuous random variable, X, has a probability density function defind by:
f(x)= o.3e-0.3x, 0<x
= 0 elsewhere

Find:
A) The mean of X
A) The median of X
A) The mode of X
A) The variance of X
A) The standard deviation of X

I have no idea where to start; any help would be really appreciated.
• Sep 3rd 2010, 10:51 PM
CaptainBlack
Quote:

Originally Posted by Supernova
A continuous random variable, X, has a probability density function defind by:
f(x)= o.3e-0.3x, 0<x
= 0 elsewhere

Find:
A) The mean of X
A) The median of X
A) The mode of X
A) The variance of X
A) The standard deviation of X

I have no idea where to start; any help would be really appreciated.

Mean:

$\displaystyle \mu=\int_D x f(x)\; dx$

where $\displaystyle D$ is the domain of $\displaystyle f(x)$

Median is the solution to:

$\displaystyle \displaymode \int_{-\infty}^x f(\xi)\; d\xi=0.5$

etc.

CB