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2.1.4 Probability densities

What if $ X$ is continuous?

Example: $ \Omega$ = population of freshman

Definition 7   A continuous random variable $ X$ has a density function $ f_X(x)$ if:

$\displaystyle P( a \le X \le b) = \int_a^b f_X(x)dx $

for every $ a$ and $ b$ ($ a \le b$).

Remarks:

  1. $ \int_{\text{range of X}} f_X(x)dx = 1 $
  2. Area under the curve gives probabilities.



Eran Borenstein
2007-05-04