[math] \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}[/math]

Write a program to carry out the following experiment. A coin is tossed

100 times and the number of heads that turn up is recorded. This experiment is then repeated 1000 times. Have your program plot a bar graph for the proportion of the 1000 experiments in which the number of heads is [math]n[/math], for each [math]n[/math] in the interval [math][35,65][/math]. Does the bar graph look as though it can be fit with a normal curve? \item Write a program that picks a random number between 0 and 1 and computes the negative of its logarithm. Repeat this process a large number of times and plot a bar graph to give the number of times that the outcome falls in each interval of length 0.1 in [math][0,10][/math]. On this bar graph plot a graph of the density [math]f(x) = e^{-x}[/math]. How well does this density fit your graph?