**The Exponential Distribution Function** is not a built-in
function on the TI-83PLUS so we will use a slightly different procedure
for calculating the area under the curve. Sometimes you want to know the
probability of an event where the occurrence of that event follows an
exponential distribution. Since it is not a function that appears on the
calculator we must enter the function. [We say x is distributed
Exponential (mu,x)]

**Example 1**

LetÕs say we want to know the probability that
this transistor will last at least 10 years if we know the life of this
transistor is distributed Exponentially with a mean life expectancy of 6
years. Here .

So our equation would be :
** (1 / 6 ) e^( - x / 6)** . On the calculator you will go to
the functions menu. Press **Y=**. ( you will see this screen)

Now we will need to enter the equation

Press
**LN**
.

(you will see this text appearing
on screen as you type.)

Now we need to adjust the WINDOW to fit our data. So press

.

These settings will
always give you a nice view of the Exponential graph.

Now on to
the graph. Press . (You will see
this graph.)

To find the area under the curve past **x=10** we will need to go
to the **Function's Calculations** menu. So press . (this screen will appear)

Arrow down to "**7 : { f (x) dx**". [This choice will integrate
the function between two points]

Now press

Now we need to enter the lower and upper limits for our problem. Since we wanted will be the lower limit and 48 will be our upper limit. 48, because our graph window only goes up to 48

We could also say [ 1 Š Integral of 0 to 10; which is 1 Š the complement. ] You will get the same answer either way.

Next, press **10**
**48** . (this screen will
appear)

This screen shows us that the area under the
curve past 10 is .18854014
So the probability that a transistor with a known life expectancy of 6 years will last at least 10 years 0.189. |

You can find the probability of any event that is distributed Exponentially using this procedure.

Recall: to clear the screen after shading you Press

"**1 : ClrDraw**" will be
highlighted, press