Solutions SM230 Final exam Spring 1997 (9 May 97)

 

  1. Calls to 911
    2.

     

    Non Amb

    Amb

     

    Fire

    0.05

    0.20

    0.25

    Police

    0.65

    0.10

    0.75

     

    0.70

    0.30

     
    1. See above
    2. 0.20
    3. 0.10/0.75=0.1333
    4. Prob(A|F)=0.20/0.25 = 0.80 > Prob(A) = 0.30, so positive corr.
    5. Prob(A|P)=0.1333 < Prob(A) = 0.30, so neg. corr.
  2. Searching
    3.

     

    A

    B

    C

     

    Detect

    0.14

    0.30

    0.09

    0.30

    Not

    0.06

    0.20

    0.21

    0.70

     

    0.2

    0.5

    0.3

     
    1. Search B. 0.30 is highest probability of detection
      2.

       

      A

      B

      C

       

      Detect

      0.203

      0.174

      0.126

      0.203

      Not

      0.087

      0.29

      0.42

      0.797

       

      0.2/0.7

      0.2/0.7

      0.3/0.7

       
    2. Search A because 0.203 is highest
  3. Blood
    1. BCDF(p=0.45,N=50,X=25)-BCDF(p=0.45,N=50,X=24)=0.08733
    2. 1-BCDF(X=25)=0.1966
    3. Solve BCDF(p=0.45,N,X=24)=0.05 -> N=70
  4. House rental
    1. BCDF(p=0.20,N=15,X=2)=0.3980
    2. Solve BCDF(p=0.20,N,X=2)=0.10 -> N=25
  5. Training tapes
    1. 1-HCDF(G=18,B=24,S=8,X=4)=0.1972
    2. HCDF(X=4)-HCDF(X=3)=0.2755
    3. HCDF(X=5)-HCDF(X=2)=0.7162
  6. Sonar
    1. 1-PCDF(L=1/5,T=1,X=0)=0.18127
    2. BCDF(p=0.18127,N=8,X=1)=0.5594
  7. Ships medical
    1. 1-PCDF(L=1/7,T=60,X=10)=0.2446
    2. 1-PCDF(L=1/7,T=1,X=0)=0.1331, by memoryless
  8. W=X+Y
    9.

    W

    Prob(W)

    1

    0.0525

    2

    0.1350

    3

    0.25

    4

    0.2750

    5

    0.1975

    6

    0.09
    1. See above
    2. 0.0525+0.1350=0.1875
    3. 1-0.0525=0.9475
    4. 3.7
    5. E(W^2)=15.42, StdDev=1.315
  9. Sub intercept
    1. 80
    2. Solve ZCDF(M=80,S=5,X)=0.01 -> 68.34
    3. Mean=140, StdDev=9.434
    4. Solve ZCDF(M=140,S=9.434,X)=0.01 -> 118.04
  10. Flight school
    1. Mean=245
    2. StdDev=8.367
    3. ZCDF(M=90,S=3,X=85)=0.0478
    4. ZCDF(M=245,S=8.367,X=230)=0.0365, Mult by 70=2.56 to fail
  11. Drug testing
    1. 50
    2. 7.036
    3. 1-ZCDF(M=50,S=7.036),X=60.5)=0.0678
    4. 0.0678
    5. 0.9322-0.0678=0.8644
    6. Solve ZCDF(M=50,S=7.036,X)=0.98 -> 64
  12. Z=X^2
    1. 12.2 = 1*0.2+9*0.4+16*0.3+36*0.1
    2. E(Z^2)=239, StdDev=9.495