STATZIKI

Exponential Probability Scale Calculator

Input








Formulas and Output

\[\beta = 2.4 \]
\[p( 0 < x < 3) = \int_{Lower X}^{Upper X} \frac{1}{\beta}e^{\frac{-X}{\beta}} dX = \int_{ 0 }^{ 3 } \frac{1}{ 2.4 }e^{\frac{-X}{ 2.4 }} = 0.7135\]
\[\begin{eqnarray*} \textrm{The function above finds the probability of the first event} \end{eqnarray*}\] \[\begin{eqnarray*} \textrm{occuring between 0 and 3 units of X given mean = 2.4 } \end{eqnarray*}\]
Probability between interval 0 and 3 = 0.7135
Probability above interval 0 and 3 = 0.2865

Example

Example, the magnitude of earthquakes recorded in a region of North America can be modeled as having an exponential distribution with mean 2.4 as measured on the Richter scale. Find the probability that the earthquake striking this region will be under 3.0 on the Richter scale.

For this question the mean is already given and the mean on an exponentially distributed variable is equal to β. To solve this we set β = 2.4, have lower X as 0 & upper X at 3.