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...
STAT 400
Hillson
TEST #2 Nov. 20, 197
r
1. Suppose X and Yare independent random variables defined on the
2.
same sample space each having geometric distribution with parameter p.
How is W = X + Y distributed?
(Hint: use moment-generating functions)
(25 points)
Suppose a system consists of 2n components arranged as follows
-<:
1,>_<1
1/ 'I
1 ",,_/I:==f) __
1/ "'1---]
Assume that the lifetime of each component is exponentially distributed
with a parameter A. Find the probability density function for the
system lifetime.
(25 points)
CONTINUED ON BACK
1
3. Suppose X and Yare random variables defined on the same sample
space with the following joint probability table
.
X""Y
0 1
0
1 1
8 4
1 3 1
8 4
(a) Compute PO' ~ X).
(b) Compute the probability mass function of the random variable
A = X + Y.
(c) Compute the marginal probability mass functions PX(x) andi Py(y).
(d) Compute Cov(X,Y).
(e) Compute the correlation PX,Y.
[25 points]
4...

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