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Department of Chemical Engineering
University of California, Santa Barbara
Ch.E.
132C
Winter, 2006
Quiz 2
1.
(
25 points
)
The joint probability density function for two random variables is
given by
f
(
x, y
) = 0.5e

x2y
for
x
> 0 and
y
> 0.
a.
(15 points)
What is the probability that 0 <
y
< 1?
b.
(10 points)
Are
X
and
Y
independent?
Justify your answer.
2.
(
25 points
)
A composite material consists of three layers of different materials,
A, B and C.
The thickness of each layer can be assumed to be normally
distributed with a standard deviation of
σ
=2 mm.
Suppose that the thicknesses of
ten
samples
are
measured
and
the
sample
means
for
each
layer,
,
, and
A
BC
X
XX
, are calculated.
a.
(10 points)
What is an unbiased point estimate of the thickness of the
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 Fall '11
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 Chemical Engineering

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