SM230 Final Exam Solutions - Fall 1996

1.

       Gold 
Silver 0.03 0.12 0.15
       0.07 0.78 0.85
       0.1 0.9 1

a 0.78

b 0.19 =0.07+0.12

c 0.2 =0.03/0.15

d 0.3 =0.03/0.10

2.

      French       Eng 
Treas 0.066666667 0.083333333 0.15
      0.6         0.25        0.85
      0.666666667 0.333333333 1 

a .15

b 0.555555556 =0.083/0.15

3.

Cave   Beach Forest 
0.1375 0.02 0.175    0.3325
0.4125 0.18 0.075    0.6675
0.55   0.2  0.25 
0.25   0.1  0.7 

a Forest

b. 0.02

c.

            0    0.02 0    0.02

1. 0.18 0.25 0.98

0.183673469=0.18/0.98

d.

0    0.02  0.175 0.195
0.18 0.075 0.805

0.683229814=0.55/0.805

4.

a. 1-BCDF(X=4,N=21,p=0.2)=0.41399

b. 31 BCDF(N=30)=0.255, BCDF(N=31)=0.2287

5.

a. HCDF(X=4)-HCDF(X=2)=0.8744-0.3111=0.5633

b. HCDF(X=N-3)-HCDF(X=2)=0.9868-0.078=0.90

N=10

6.

a. 1-PCDF(L=1/3.5,T=7,X=2)=0.32332

b. 0.135335

c. Solve 1-PCDF(X=0,T=?)=0.90

T=8.1

7. PCDF(L=1/5,T=30,X=3)=0.151

There is a 15% chance of running out of supplies.

8.

a. PCDF(L=1/12,T=10,X=0)=0.434598

b. PCDF(L=1/12,T=20,X=2)=0.765995

9.

a. 0.4

b. (0.6)^8=0.016796

10.

a. 1-ZCDF(M=100,S=15,X=120)=0.091211

b. 135

c. 470

11.

Mean 1.2

E(X^2) 2.1

S.D. 0.81240384

c. ZCDF(X=101.5)=0.011387

d.

5 0.03

6 0.0025

ANS= 0.0325