Math 285: Solutions of Homework V
Exercise for Chapter 1
1
1. Solution. The expectation is 6 .
1
2. Solution. Similar to problem 1, the expectation of each asset to trade for is 6 . And
in sum, it will be 1.
3. Solution. The price will actually decrease.
Math 285: Solutions of Homework IV
Exercise for Section 3.4
1. Solution. Let Ij be the indicator function of the event that the outcome of the j + 1th
toss is dierent from the outcome of he jth toss. THe number R if distinct runs is given
n1
by R = 1 + j=
Math 285: Solutions of Homework VII
Exercise for Section 5.7
7. Proof. If X is N(, 1), then the moment generating function of X 2 is
2
MX 2 (s) = E(esX ) =
2 s
1
1
1
2
2
esx e 2 (x) dx =
e 12s ,
1 2s
2
if s < 1 , by completing the square in the exponent.
Math 285: Solutions of Homework VI
Exercise for Chapter 2
2. Solution.
(i) 0 C 1.
(ii) C = S 80. Hence the lower bound is 0 and there is no upper bound.
(iii) 0 C 20.
(iv) It is similar to (ii), the lower bound is 0 and there is no upper bound.
3. Solutio
Math 285: Solutions of Homework II
Some problems of this homework set is really challenging, such as 1.4.5, 1.8.19 and 1.8.21.
And although 1.4.6 is an easy problem, its background, the law case the authors mentioned in the textbook, is surprisingly inter
Math 285: Solutions of Homework I
Exercise for Section 1.2
1. Proof. Here we only prove (i Ai )c = i Ac . The proof for (i Ai )c = i Ac is similar.
i
i
For x (i Ai )c , we know that x i Ai . So x Ai for any i. Hence x Ac for any
/
/
i
i, which implies tha