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{SECT 0 {PARA 18 "" 0 "" {TEXT -1 25 "The Central Limit Theorem" }}
{PARA 256 "" 0 "" {TEXT -1 769 "This routine generates n iid Bernoulli
 random variables with success probability 0.6, forms their sum S, and
 does this m times, plotting the resulting m numbers with a histogram.
 When n is large the central limit theorem tells us that S should be a
pproximately normal with mean .6n and variance .24n. On the same axes \+
is plotted the corresponding theoretical normal density. You can inves
tigate the effect of n on the shape of the resulting distribution by c
hanging its value below ; the program only works for n \263 14 however
. You can also change m, whose effect is simply the accuracy of the pi
cture you get; you'd like to have m large to get an accurate represent
ation of the distribution of S for a fixed n, but making m large requi
res more time to see the picture. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 813 "with(stats):\n m := 250;\n \+
 n := 30;\n### WARNING: persistent store makes one-argument readlib ob
solete\nseed := readlib(randomize)():\n randomize(abs(seed)):\n  v := \+
array(1..m):\n for k to m do\n s := 0:\n \011\011\011for j to n do\n \+
\011\011\011x := 0:\n  \011\011\011y := evalf((rand())/999999999999):
\n  \011\011\011if ( y < 0.60) then x := 1 fi:\n  \011\011\011s := s+x
:\n  \011\011\011od:\n v[k] := s:\n od:\n   S := [seq(v[k],k=1..m)]:\n
bg := floor(.6*n-3*sqrt((.24)*n)):\nnd := floor(.6*n+3*sqrt((.24)*n)):
\n#dlt := floor((nd-bg)/11):#\ntld := transform[tallyinto](S,[0..bg+.5
,seq(i-1+ bg+.5..i +bg+.5, i= 1..nd-bg),nd +.5..n]):\n### WARNING: the
 statplots sub-package has been completely rewritten; see the help pag
es for details\nstatplots[histogram](tld,colour=yellow):plot(m*stats[s
tatevalf,pdf,normald[.6*n,sqrt((.24)*n)]],0..n,colour=red,thickness=2)
:plots[display](\{%,%%\});\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
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{PAGENUMBERS 0 1 2 33 1 1 }