CEE 304  Uncertainty Analysis in Engineering
Second Examination
November 12, 2004
You may use text, your notes and calculators. There are 50 points in total, one per minute.
1. (6 pts)
True or false, and short answers.
a. The sample average is
always
an
unbiased estimator
of the population mean: ___ (true or false).
b. The sample average of n observations has a standard deviation equal to
σ
/n: ___ (true or false).
c. The sample variance is
always
an
unbiased estimator
of the population variance: ___ (true or false).
d. If the data is normally distributed, the variance of the sample variance is ________ .
e. Given the mean and variance of an estimator, its mean square error is equal to ________ .
f. A good distribution to describe the smallest of many values bounded below by zero is the ___ distribution.
2. (10 pts) For a decorative display, a company produces brightly colored circles that have radii that are
lognormally distributed with mean 5.0 and standard deviation 2.0. However, interest is not in R, but the area
of the circles given by A = 3.14 R
2
. Using the properties of the lognormal distribution, what are the mean and
coefficient of variation of A?
3. (6 pts) In a pharmaceutical firm, a quality control program collects 16 samples a day to ensure that a
number of chemical parameters are within tolerances. For example, on Tuesday the sample mean and sample
standard deviation of the 16 nitrate observations were 2.67 mg/l and 0.14 mg/l. Based on that information,
what is a 99% confidence interval for the
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 Fall '08
 Stedinger
 pts, Maximum likelihood, Estimation theory, Likelihood function, Ri

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