Probabilities are areas under the curve

• Areas under the curve correspond to the probability of a value falling into the relevant interval.

• For instance, 50% of the time, a $\chi ^2$ variable with DF of 5 will be in the range 0-4.35. 99% of the time the value will fall under 15.09, meaning that there is only a 1% chance of getting a random $\chi ^2$ variable with 5 degrees of freedom above this level.

  $\parbox{\textwidth}{\includegraphics{chi-dist.eps} \par \centerline{Areas under the curve and probabilities}}$