Working data will be in C:\Program 
Files\sp2000\users\default\_Data 
# This exercise is based on Example 1.4.1 in Lehmann.
> binomsamp_function(n,p,a,b)
+ {x_rbinom(1000,n,p)
+ (a+x)/(a+b+n)
+ }
> s50_binomsamp(50,.2,1,1)
> length(s50)
[1] 1000
> s50[1:10]
 [1] 0.2115384615384615 0.1538461538461538 0.1538461538461538
 [4] 0.1730769230769231 0.1730769230769231 0.2692307692307692
 [7] 0.2307692307692308 0.1538461538461538 0.2307692307692308
[10] 0.1923076923076923
> s200_binomsamp(200,.2,1,1)
> s1000_binomsamp(1000,.2,1,1)
> bias_c(mean(s50),mean(s200),mean(s1000))-.2
#  The bias variable is an estimate of the true bias,
#  based on a random sample of size 1000.
> bias
[1] 0.0105192307692305900 0.0018316831683166940 0.0008922155688623479
> variance_c(var(s50),var(s200),var(s1000))
#  The variance variable is an estimate of the true variance,
#  based on a random sample of size 1000.
> variance
[1] 0.0028905351357274420 0.0007597809553500175 0.0001660354582892740
> n_c(50,200,1000)
> n
[1]   50  200 1000
> bias*n
[1] 0.5259615384615293 0.3663366336633389 0.8922155688623479
> bias*n^2
[1]  26.29807692307646  73.26732673266778 892.21556886234780
> bias*sqrt(n)
[1] 0.07438219409789129 0.02590391178603990 0.02821433361467825
# Bias seems to be of order 1/n or 1/root(n), certainly not of
# order 1/n^2.
> variance*n
[1] 0.1445267567863721 0.1519561910700035 0.1660354582892740
> variance*n^2
[1]   7.226337839318605  30.391238214000700 166.035458289274000
# Variance seems to be of order 1/n, certainly not 1/n^2.
>