STAT 100A HWI Due next Wed in class
Problem 1:
Suppose we flip a fair coin 4 times independently.
(1) What is the sample space?
(2) What is the set that corresponds to the event that the number of heads is 2? What is its
probability?
(3) Let
Z
i
= 1 if the
i
th flip is head, and
Z
i
= 0 otherwise, for
i
= 1
,
2
,
3
,
4. Let
X
be the
number of heads. Express
X
in terms of
Z
i
.
(4) What is the probability distribution of
X
? That is, what is Pr(
X
=
k
) for
k
= 0
,
1
,
2
,
3
,
4?
Problem 2:
Suppose we roll a fair die twice independently. Let
X
and
Y
be the two numbers we
get.
(1) What is the sample space? Let
A
be the event that
X >
4, and
B
be the event that
Y >
4.
What are Pr(
A
), Pr(
B
)?
(2) Let
C
be the event that min(
X, Y
)
>
4? What is Pr(
C
)? What is the relationship between
Pr(
C
) and Pr(
A
), Pr(
B
)?
(3) Let
D
be the event that max(
X, Y
)
>
4? What is Pr(
D
)? What is the relationship between
Pr(
D
) and Pr(
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 Fall '07
 Wu
 Probability, Probability theory, Randomness, Probability space

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