Theorem: For any interger n ≥ 1 , ∑ t = 1 n i ( i ! ) = ( n + 1 ) ! − 1 "Proof (by mathematical induction): Let the property P ( n ) be ∑ t = 1 n i ( i ! ) = ( n + 1 ) ! − 1 Show that P (1) is true. When n = 1,
Theorem: For any interger n ≥ 1 , ∑ t = 1 n i ( i ! ) = ( n + 1 ) ! − 1 "Proof (by mathematical induction): Let the property P ( n ) be ∑ t = 1 n i ( i ! ) = ( n + 1 ) ! − 1 Show that P (1) is true. When n = 1,
Solution Summary: The author explains how to determine the errors in the proof fragments. Circular reasoning assumes that P (1) is true when we need to prove it.
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"Proof (by mathematical induction): Let the property
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Show that P (1) is true. When n = 1,
A television network earns an average of $14 million each season from a hit program and loses an average of $8 million each season on a program that turns out to be a flop. Of all programs picked up by this network in recent years, 25% turn out to be hits and 75% turn out to be flops. At a cost of C dollars, a market research firm will analyze a pilot episode of a prospective program and issue a report predicting whether the given program will end up being a hit. If the program is actually going to be a hit, there is a 75% chance that the market researchers will predict the program to be a hit. If the program is actually going to be a flop, there is only a 30% chance that the market researchers will predict the program to be a hit.
What is the maximum value of C that the network should be willing to pay the market research firm? Enter your answer in dollars, not in million dollars.
$ __________
Calculate EVPI for this decision problem. Enter your answer in dollars, not in million…
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