oddities

The EL9600 appears to have a few quirks, particularly on the programming side! If any of this is incorrect - or correctable - please let MathsNet know.

Randomness

0->Xmin
10->Xmax
0->Ymin
10->Ymax
0->N
Label LL
N+1->N
10*random->A
10*random->B
PntOn(A,B)
If N<200 Goto LL

This will select at random 200 pairs of coordinates and plot them on a graph with axes ranging from 0 to 10. You would expect to see a fairly random display, something like:

However, you don't - at least on my calculator. Instead you get columns of scattered points. Change the 10th line to read

PntOn(B,A)

10*random->A
random->B
10*random->B

Clearing the GRAPH screen

A PLOT1
B PLOT2
C PLOT3
D LIMIT
E ON/OFF

statistical functions

The binomial distribution

The Binomial distribution requires two parameters, n and p. Assume n=4. Either estimate p from the above data (p=mean/n=0.5125) or use an assumed value. In the calculator, select

pdfbin(4,0.5125)

You will find this in the STAT menu, option F, option 09. The calculator will display in a sequence the probabilities of 0 to 4 successes:
{.0564804932 .2375077148 .3745313965 .2624920898 .0689883057}
You can scroll along the sequence using the arrow keys. Now enter:

x 20

and a sequence of the expected frequencies will be displayed (here shown rounded to 1 dp):
{1.1 4.8 7.5 5.2 1.4}
These can be compared with the observed frequencies in the above table (and tested if you like with the chi-squared test).

The Poisson distribution

poipdf(2.05,{0,1,2,3,4})

You will find this in the STAT menu, option F, option 11. Note the use of the two kinds of brackets () and {}. The calculator will display in a sequence the probabilities of 0 to 4 successes:
{.1287349036 .2639065524 .2705042162 .1848445477 .097328307}
These probabilities give the following expected frequencies:
{2.6 5.3 5.4 3.7 1.9}

The Normal distribution

cdfnorm(-1E99,3,2.05,2)

You will find this in the STAT menu, option. F, option 02. This is a little cumbersome as you must enter -1E99 or -1 x 10⁹⁹ to indicate negative infinity. The calculator should display 0.68

If you wish to find probabilities from the standard normal distribution, ie., N(0,1), then you can simply enter

cdfnorm(-1E99,3)

to find the probability P(Z<3).

Here is a standard text book example on Normal probabilities:
IQ scores are assumed to be normally distributed with mean 100 and standard deviation 15. Find the perecentage of people expected to have an IQ between 80 and 120.

Answer
cdfnorm(80,120,100,15)=0.8175... or 81.75%

Solving problems on the Normal distribution

Answer
The question implies that P(Z < Z₀)=0.95, where Z₀=-(250 - x)/1.5

Use the InvNorm function (in the STAT menu, option F, option 03) to calculate:

InvNorm(0.95)=1.644853626

Hence 1.644853626=-(250 - x)/1.5, which gives x=252.46...

Displaying probability distributions

The EL-9600 can be set up to display a distribution. For example, taking n=7 and p=0.2, then this binomial display can be obtained: To do this enter these instructions: {0,1,2,3,4,5,6,7}->L1 pdfbin(7,0.2)->L2 STAT PLOT A PLOT1 Select on, DATA X, LISTX:L1, Freq:L2 WINDOW Select Xmin=0, Xmax=7, Xscl=1, Ymin=0, Ymax=.5, Yscl=.1 GRAPH

downloadable files

COMPLX

Label START
Print "Inputs ARe...
Print "1.Polar
Print "2.RectAnGuLAR
Print "			"spacing for aesthetics and clarity
Input A
ClrT
Print "1.ADD
Print "2.SuBtRACt
Print "3.MuLtIpLY
Print "4.DIvIDe
WAIt3
ClrT
Print "COnveRt tO...
Print "
Print "5.Polar
Print "6.RectAnGuLAR
Print "			"spacing for aesthetics and clarity
Input B
(A+1)¾A			"first stage of creating unique ref code
(A^4)+(3B)¾C		"create unique reference code
ClrT
If A=2Goto InputPOL	"get polar inputs for calculation
If A=3Goto InputReC	"get rectangular inputs for calculation
Goto START

Label InputPOL
Print "Input 1st vALues
Input R
Input ©
ClrT
Print "Input 2nD vALues
Input P
Input Q
ClrT
Goto FUNCTION

Label InputReC
Print "Input 1st vALues
Input X
Input Y
ClrT
Print "Input 2nD vALues
Input V
Input W
ClrT
Goto FUNCTION

Label FUNCTION
If C=19Goto POLCOnv	"use unique code to go to next stage
If C=84Goto ReCADD
If C=22Goto POLCOnv
If C=87Goto ReCSuB
If C=25Goto POLMLtpLY
If C=90Goto ReCCOnv
If C=28Goto POLDIv
If C=93Goto ReCCOnv
If C=96Goto ReCCOnv
If C=34Goto POLCOnv
Goto ERROR

Label ERROR		"safeguard against incorrect values entered in A + B at 
start
Print "ERRor In CHOICes
Print "stARt AGAIn
End

Label ReCCOnv
xyØr(X,Y)¾R		"convert rectangular co-ords to polar
xyØ©(X,Y)¾©
xyØr(V,W)¾P
XY Q(V,W)¾Q
If E=2Goto OUTPUTRO	"used as part of OUTPUT
If C=90Goto POLMLtpLY	"used as part of OUTPUT
If C=93Goto POLDIv	"used as part of OUTPUT
If C=96Goto OUTPUTRO	"used as part of OUTPUT

Label POLCOnv
r©Øx(R,©)¾X		"convert polar co-ords to rectangular
r©Øy(R,©)¾Y
r©Øx(P,Q)¾V
r©Øy(P,Q)¾W
If E=6Goto OUTPUTXY	"used as part of OUTPUT
If C=19Goto ReCADD	"used as part of OUTPUT
If C=22Goto ReCSuB	"used as part of OUTPUT
If C=34Goto OUTPUTXY	"used as part of OUTPUT

Label ReCADD
ClrT
X+V¾X
Y+W¾Y
1¾E			"first stage of creating unique code for OUTPUT
Goto OUTPUT

Label ReCSuB
ClrT
X-V¾X
Y-W¾Y
1¾E			"first stage of creating unique code for OUTPUT
Goto OUTPUT

Label POLMLtpLY
ClrT
R*P¾R
©+Q¾©
4¾E			"first stage of creating unique code for OUTPUT
Goto OUTPUT

Label POLDIv
ClrT
R/P¾R
©-Q¾©
4¾E			"first stage of creating unique code for OUTPUT
Goto OUTPUT

Label OUTPUT
ClrT
Print "SeLeCt Output
Print "tYpe
Print "			"spacing for aesthetics and clarity
Print "1.Polar
Print "2.RectAnGuLAR
Print "			"spacing for aesthetics and clarity
Print "			"spacing for aesthetics and clarity
Input D
D+E¾E			"create unique code for RECADD, RECSUB, POLMLTPLY & POLDIV
If E=2Goto ReCCOnv
If E=3Goto OUTPUTXY
If E=5Goto OUTPUTRO
If E=6Goto POLCOnv
Goto OUTPUT

Label OUTPUTXY
0¾E			"ensure D is zero ready for next program use (reduce risk of 
errors)
ClrT
Print "X=
Print X
Print "Y=
Print Y
End

Label OUTPUTRO
0¾E			"ensure D is zero ready for next program use (reduce risk of 
errors)
ClrT
Print "MODuLus =
Print R
Print "ARGuMent =
Print ©
End

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