Improvements in Graphics from 1967 - present at Hope College,. Prepared by Elliot A. Tanis August, 2009. IBM 1130 Computer Purchased in 1967. A web site: http://ibm1130.org/
Elliot A. Tanis
Pairs of “random numbers” generated by our improved version of a pseudo random number generator.
In her independent project report on May 25, 1968, she included an illustration of the Central Limit Theorem using a U-shaped distribution with p.d.f. f(x) = (3/2)x^2, -1 < x < 1. Not only did she do the simulation, but she also wrote some graphics programs to see what was happening. Some of her output from the line printer is included on the next slide.
This example is used to illustrate improvements in graphics.
Here is a graph of the p.d.f. and the FORTRAN program that will do the simulation.
This graph shows output for samples of size 1 to confirm that we are indeed sampling from this U-shaped distribution.
This parent distribution has been used in many presentations throughout my tenure at Hope College, culminating is the use of MAPLE and finding the theoretical p.d.f.
For -1 < x < 1,
A plotter is used for the histogram and the N(0,1) p.d.f. is superimposed.
TRS-80 graphics: (1984) U-shaped distribution, March, 1969This figure shows the distribution of the sample mean when sampling from a U-shaped distribution for n = 2, 5, and 8.
IBM PC graphics: U-shaped distribution, March, 1969 Comparison of t and z confidence intervals for the mean. How many rolls of a 20-sided die are needed to observe at least one of its faces twice? Graph compares theoretical and empirical histograms.“Computer Simulations to Motivate and/or Confirm Theoretical Concepts” (1987)
The laboratory for mathematical statistics and probability incorporated MAPLE and MINITAB. This manual was published in 1995 by Prentice Hall.
Here is output from a talk given at the Joint Statistics Meetings in Dallas, 1998. This was prepared using MAPLE V, comparing simulated data and the theoretical p.d.f.
Use Meetings in Dallas, 1998. This was prepared using MAPLE V, comparing simulated data and the theoretical p.d.f.MAPLE to find p.d.f.s of sums of independent random variables. This example uses the U-shaped distribution introduced by Deanna Gross in 1968, finding p.d.f.s of the sums of random samples of sizes 2, 3, 4.
For -1 < x < 1,