Test 3 Questions
1.
If
is an exponential random variable with pdf
Y
( )
exp{
/ 3}/ 3,
0
fy
y
y
=
−>
,
then find a number
t
(to three decimals) so that
.
(
)
0.05
PY t
>=
2.
Suppose
are independent exponential random variables with mean
1
100
,...,
YY
2
θ
=
and
.
Use the central limit theorem to estimate
.
100
1
j
j
S
=
=
∑
Y
0
(
200  20)
PS
3.
Suppose
is a standard gaussian random variable. Find a number
c
(to
three decimals)
so that
.
~(
0
,
1
)
ZG
()
0
.
2
PZ c
4.
We are given that
and
12
0
,...,
~
(0,1), independent
ZZG
1
i
a
= +
is
i
is even and
if
i
is odd. Then if
, find (to three decimals)
.
1
i
a
=−
20
1
(1
)
i
i
Ta
Z
=
=+
∑
i
(
2)
PT
>
5.
Suppose we can model the number of claims per week of a certain type of
insurance policy as a Poisson random variable with mean
λ
. In a 10 week period,
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 Spring '10
 McKay
 Decimals, Normal Distribution, Probability theory, exponential random variable

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