PSTAT 120A, Spring 2010, Practice Final.
(1) (a) Let
X
and
Y
be independent random variables each having
the probability mass function
p
(
x
) =
1
2
2
3
x
,
x
= 1
,
2
,
3
, . . .
Find
P
(
X
= 1
, Y
= 3) and
P
(
X
+
Y
= 3).
(b) Let
X
and
Y
be two independent random variables with
the same probability density function given by
f
(
x
) =
(
e

x
if 0
< x <
∞
0
elsewhere.
Show that
g
, the probability density function of
X/Y
, is given
by
g
(
t
) =
(
1
(1+
t
)
2
if 0
< t <
∞
0
t
≤
0
.
(2) According to the US National Center for Health Statistics,
25.2% of males and 23.6% of females never eat breakfast. Sup
pose that random samples of 200 men and 200 women are cho
sen. Approximate the probability that
(a) at least 110 of these 400 people never eat breakfast;
(b) the number of the women who never eat breakfast is at least
as large as the number of men who never eat breakfast.
(3) The monthly worldwide average number of airplane crashes of
commercial airlines is 2.2. What is the probability that there
will be
(a) more than 2 such accidents in the next month?
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 Spring '10
 RohiniKumar
 Probability, Variance, Probability theory, probability density function

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