A random sample will be drawn from a normal distribution, for the purpose of estimating the population meanµ. Since µ is the median as well as the mean, it seems that both the sample median m and the sample mean 
are reasonable estimators. This exercise is designed to determine which of these estimators has the smaller uncertainty.
a. Generate a large number (at least 1000) samples of size 5 from a N(0, 1) distribution.
b. Compute the sample medians 
for the 1000 samples.
c. Compute the mean m and the standard deviation of 
d. Compute the sample means 
for the 1000 samples.
e. Compute the mean and standard deviation 
f. The true value of µ is 0. Estimate the bias and uncertainty 
in m.
g. Estimate the bias and uncertainty 
. Is your bias estimate close to 0? Explain why it should be. Is your uncertainty estimate close to 
? Explain why it should be.
(a,b) Answers will vary.
(c) 
= (simulation results will be approximate), 
.
(d) Answers will vary.
(f) Bias is exactly 0 in both cases (simulation results will be approximate). exactly 
(simulation results will be approximate).
(g) Bias estimate should be close to 0 because 
so the true bias is 0. The uncertainty should be close to
because 
.
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