Prof. Edwin Romeijn
ESI 6321 Applied Probability Methods For Engineers
Homework 1 - Solutions
Spring 2008
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ESI 6321 APPLIED PROBABILITY METHODS FOR ENGINEERS
Homework 1 – Spring 2008
Solutions
Exercise 2.2
(a) A total of 8 outcomes: HHH, HHT, HTH, HTT, THH, THT, TTH, and TTT.
(b) P(HHT) = 1/8.
(c) P(First two tosses are heads) = 2/8.
(d) P(Two heads in a row) = 3/8.
Exercise 2.6
Time Slot
Ad Cost
Estimated
Viewers
Estimated
Earnings
Expected
Net Profit
Morning
$120,000
1,000,000
$160,000
$40,000
Afternoon
$200,000
1,300,000
$208,000
$8,000
Prime Time
$400,000
3,200,000
$512,000
$112,000
Late Evening
$150,000
800,000
$128,000
-$22,000
(a) According to the table above, the prime time slot would yield the highest expected
net profit, $112,000.
(b) The company should buy the morning and the prime time slots, with a total
expected contribution to earnings of $152,000.
Exercise 2.10
Let S1 denote the lamp comes from first shipment, S2 denote the lamp comes from
second shipment, and D denote the lamp is defective. We want to compare P(S1 | D)
to P(S2 | D). We have P(S1) = 100/150 = 2/3, P(S2) = 50/150 = 1/3, P(D | S1) = 0.04,