The Exponential Distribution Function

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