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SW text Sec 3.2, Random Sampling
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> #ex 3.1 text, draw random uniform, discrete
> #Ex3.1 SW, use 'sample' to get 15 obs from discreteU[1,2500] no replacement
> k = 1:2500
> sample(k, size = 15, p = rep(1:1, 2500)/2500)
 [1] 1403 2008 1467 1883  454  369 1551 1174 1881 2348   31 1752 1545 2441  484
> sample(k, size = 15, p = rep(1:1, 2500)/2500)
 [1] 1480  501  723  675 1372  941 1740   12 2457 1282 1549 1166 1558 1191  251
> sample(k, size = 15, p = rep(1:1, 2500)/2500)
 [1] 2298 1752  307 1574  175 1921 2225  882 1908 1328  996 2074 2326  381 1128
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Illustrate Rectangular Distribution
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> stem(sample(k, size = 1500, p = rep(1:1, 2500)/2500, replace = T))
   output deleted
> #each bin/stem has about 60
> hist(sample(k, size = 1500, p = rep(1:1, 2500)/2500, replace = T))
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> #sampling exercise, number of mutants, p.77-78
> k = 0:99
> sample(k, size = 5, p = rep(1:1, 100)/100)
[1] 54 49 42 31 67
> sample(k, size = 5, p = rep(1:1, 100)/100)
[1]  5 64 82 58 43
> sample(k, size = 5, p = rep(1:1, 100)/100)
[1] 23 33  6 88 29
> sample(k, size = 5, p = rep(1:1, 100)/100)
[1]  1 52 39 15  9
> sample(k, size = 5, p = rep(1:1, 100)/100)
[1] 62 94 13 43 68
> #42 and 67 mutants in my first try
> help("sample")
Description:
 'sample' takes a sample of the specified size from the elements of
 'x' using either with or without replacement.
Usage:
  sample(x, size, replace = FALSE, prob = NULL)
> help("rep")
>Description:
 'rep' replicates the values in 'x'. 
Usage:
 rep(x, times, ...)
> rep(1:5,2)
 [1] 1 2 3 4 5 1 2 3 4 5
probability examples SW Text, Sec 3.3-3.5
> # verzani ex 5.1 number heads in 2 tosses
> k = 0:2
> p = c(1,2,1)/4
> sample(k, size=10, prob = p, replace = TRUE)
 [1] 2 1 0 1 2 0 1 0 0 2
> try1 = sample(k, size=100, prob = p, replace = TRUE)
> table(try1)/100
try1
   0    1    2 
0.26 0.48 0.26 
> try1 = sample(k, size=1000, prob = p, replace = TRUE)
> table(try1)/1000
try1
    0     1     2 
0.234 0.518 0.248 
> try1 = sample(k, size=1000, prob = p, replace = TRUE)
> table(try1)/1000
try1
    0     1     2 
0.252 0.498 0.250