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(ISOM111)[2008](f)midterm~2546^_10369.pdf
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Solution (2008)
1. (a) 0.003
(b)
Generally speaking, it is bell-shaped with mean and median very close to zero. Smaller relative changes are more frequent than larger changes, except for large relative changes (> 2% and <-2%). There are more positive relative changes. There are more large losses than large gains.

(c)
Most likely, he would have a profit because there are more positive relative changes.

(d)
There are more large losses. The magnitude of large losses is also larger than that of large gains.


2. (a) 0.3+0.2+0.1 = 0.6
(b)
0.2/(0.2+0.1+0.1) = 0.5

(c)
(0.2+0.1)/ (0.3+0.2+0.2+0.1)= 0.375

(d)
0.6*90%+0.4*60%=78%.


3. (a) (0.9-0.78)2*0.6+(0.6-0.78)2*0.4=0.0216
(b)
0.5*3+0.3*2.5+0.2*2=2.65

(c)
Z = X*Y

(d)


Value 2.7 2.25 1.8 1.5 1.2
Probability 0.3 0.2 0.3 0.1 0.1

321
4. (a) C2 (0.8) (0.2) = 0.384
(b)
1 C 0.6*0.6 = 0.64
P(T = 3) = P(F = 2, L = 1) + P(F = 3, L = 0) + P(F = 1, L = 2)


(c)

= 0.384 0.48 + 0.512 0.16 + 0.096 0.36 = 0.3008

(d)
0.8*3+0.6*2 = 3.6


5. (a) Let X be the random net profit from a performance seeker P{X> 430} = P{Z > (430 . 450) / 50} = P(Z >.0.4) = 0.5 + 0.1554 = 0.6554
(b) Let Y be the random net profit from a bargain seeker
P(X < 350) 0.3 + P(Y < 350) 0.7 = P(Z <.2) 0.3 + P(Z < 1) 0.7

.= 0.0228 0.3 + 0.8413 0.7 = 0.59575
(c)
0.3*450+0.7*320 = 359

(d)
p 450 + (1. p) 320 = 350 . p = 0.231

(e)
Q =.0.67,Q = 0.67 , H . Spread = Q . Q ,


13 31
upper inner fence =0.67+1.5(1.34) s.d. = 2.68 s.d. lower inner fence = -2.68 s.d. P(.2.68 < Z < 2.68) = 0.0037 2 = 0.0074