ENGM2032, Applied Probability and Statistics
Winter 2010
Assignment #4
Due:
Tue Feb 7, 2010
1) Four cards are dealt from a shuffled deck of 52 cards.
Let
X
count the number of spades
appearing in the four dealt cards.
a) What is the probability mass function for
X
?
b) What is the expected value of
X
?
2) A company has determined that the drilling depth
X
, in metres, before encountering oil in a
certain region is random and distributed according to
f
X
(
x
) = 0
.
002
e

0
.
002
x
for
x
0
a) What is the probability that the next well drilled will encounter oil at a depth exceeding
700 m?
b) Out of the next 7 wells drilled, what is the probability that exactly three of them exceed
700 m in depth before striking oil?
3) Suppose that by rounding the records, the following discrete probability mass function has
been determined for the average temperature,
T
in
o
C, in Halifax over the month of March:
t
6
4
2
0
2
4
P
T
=
t
0.10
0.10
0.30
0.25
0.15
0.10
Find the following;
a) P
T
0 ,
b) P
4
< T <
4 ,
c) compute
F
T
(
t
) and sketch its graph,
d) compute E
T
,
e) compute Var
T
.
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 Spring '10
 yao
 Probability distribution, Probability theory, probability density function, Cumulative distribution function, Probability mass function

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