EMIS 7300

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EMIS 7300

• SE4 Quiz 2

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Problem 1

• Assume the first digit may be zero.
• Each digit is equally likely to be 0, 1, 2, , 9.
• Use a binomial distribution.
• A) n 7, r 2, p 0.1, probability 0.1240
• B) n 7, r 1, p 0.4, probability 0.1306

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Problem 2

• Let X be the ACT score of a randomly selected
  high school senior in DISD.
• X N(22,2)
• A) P(X gt 26) P(Z gt (26-22)/2) where Z N(0,1)
• P(Z gt 2) 1 P(Z lt 2) 1 0.97725
  0.02275
• 2.275 of DISD students are potential
  engineering recruits.
• B) P(X lt 17) P(Z lt (17-22)/2) P(Z lt -2.5)
• P(Z lt -2.5) P(Z gt 2.5) 1 P(Z lt 2.5)
  0.00621
• 0.621 of DISD students are not eligible.

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Quiz 2 Problem 3

• Random Events
• E ? Earthquake at Diablo Canyon in the next five
  years
• F ? No earthquake at Diablo Canyon in the next
  five years
• PE ? Geologist predicts an earthquake at Diablo
  Canyon
• PF ? Geologist predicts no earthquake at Diablo
  Canyon
• P(PEE) 0.95, P(PFE) 0.05
• P(PFF) 0.90, P(PEF) 0.10

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Problem Calculated Probabilities
P(PE) 0.19 0.08 0.27
P(EPE) 0.19/0.27 0.70
P(PF) 0.01 0.72 0.73
P(FPF) 0.72/0.73 0.99
P(E and PE) 0.19
PE
0.95
PF
E
P(E and PF) 0.01
0.05
0.20
F
PF
P(F and PF) 0.72
0.90
0.80
PE
0.10
P(F and PE) 0.08
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Decision Tree w/o Geologist
EMV(1) (0.2)(-30M) (0.8)(-10M) -14M
-30M
Diablo
-10M
Springfield
-20M
Without consulting the geologist, the optimal
decision is to build the plant at Diablo Canyon.
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Decision Tree for Consulting the Geologist
EMV(3) (0.7)(-31M) (0.3)(-11M) lt - 21M
-31M
Diablo
-11M
PE (0.27)
Springfield
-21M
-31M
Diablo
PF(0.73)
-11M
Springfield
-21M
EMV(4) (0.01)(-31M) (0.99)(-11M) - 11.2M
EMV(2) (0.27)(-21M) (0.73)(-11.2M) gt -
13.85M
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Optimal Policy

• EMV(No Geologist) -14,000,000
• EMV(w/Geologist) -13,846,000
• Conclusion (Based on Maximum EMV)
• Pay for the geologists prediction
• If he predicts an earthquake build at
  Springfield. Otherwise, build at Diablo Canyon.