# basic question on distribution equations

• April 8th 2011, 03:40 PM
Sneaky
basic question on distribution equations
if i have a exponential distribution equation for example, and i want to know the probability of a certain region between x1 and x2, would all i have to do is get the cdf equation, then plugin lambda, then subtract this equation with a x2 value, with the same equation with a x1 value, to get the probability between x1 and x2?

so

and of course i set lamdba.
cdf(x2) - cdf(x1) = probability between x1 and x2?

Does this work with any distribution equation weather discrete or continuous?
• April 8th 2011, 04:28 PM
SpringFan25
You need to be careful with your definition of "between x1 and x2" for the discrete case. The following is true for any discrete or continuous distribution:

$P(a < X \leq b) = cdf(b) - cdf(a)$

for most* continuous variables, its true that
$P(a < X) = P (a \leq X)$ and so you can say

$P(a \leq X \leq b) = cdf(b) - cdf(a)$ for those cases

*some continuous variables are on a mixed distribution has a probability mass at a fixed point, so the last part may not work for those.