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(b) Expected value of [Cn] ~

(b) Expected value of [Cn] ~

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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which in this case becomes 10 1 expected value 5. [Cn] · p([(Cn)) d[Cn]. 10 - Help the scientists estimate this integral. (a) First, the units of the expected value are! To do this: image 2 • You might want to change the input variable from [Cn] to x to make it easier to parse the integrals; • Use integration by parts to simplify the formula for the expected value so that you can use the information on the table above; • Use a left-hand Riemann sum on the remaining integral with 3 intervals to compute it. (b) Expected value of [Cn] ≈~¯
Transcribed Image Text:which in this case becomes 10 1 expected value 5. [Cn] · p([(Cn)) d[Cn]. 10 - Help the scientists estimate this integral. (a) First, the units of the expected value are! To do this: image 2 • You might want to change the input variable from [Cn] to x to make it easier to parse the integrals; • Use integration by parts to simplify the formula for the expected value so that you can use the information on the table above; • Use a left-hand Riemann sum on the remaining integral with 3 intervals to compute it. (b) Expected value of [Cn] ≈~¯
Two chemists created a new way to convert unobtainium [Uo] into canotainium [Cn]. After many experiments, they gathered some data about the probability of producing specific amounts of [Cn] at the end of one run of the conversion process. This is their data: and [Cn] (in mg) po 2 7 10 0 0.07 0.13 0.16 0.21 Here: dp d[Cn]' p([Cn]) is the probability of ending up with [Cn]mg of canobtainium after one run of the conversion process. The chemists also know that: • There is 0.07 probability of finishing the conversion process with no [Cn], and • There is a 0.69 probability of finishing the conversion process with 10mg of [Cn]. They need to compute the expected production of [C'n] over one run of the conversion process. Because the rate of change is continuous (even though the data they gathered is not), they decide to use a formula they found in an old dusty statistics textbook: expected value= [*[Cn] ·p([Cn)) d[Cn], 1 ba image 1 which in this case becomes
Transcribed Image Text:Two chemists created a new way to convert unobtainium [Uo] into canotainium [Cn]. After many experiments, they gathered some data about the probability of producing specific amounts of [Cn] at the end of one run of the conversion process. This is their data: and [Cn] (in mg) po 2 7 10 0 0.07 0.13 0.16 0.21 Here: dp d[Cn]' p([Cn]) is the probability of ending up with [Cn]mg of canobtainium after one run of the conversion process. The chemists also know that: • There is 0.07 probability of finishing the conversion process with no [Cn], and • There is a 0.69 probability of finishing the conversion process with 10mg of [Cn]. They need to compute the expected production of [C'n] over one run of the conversion process. Because the rate of change is continuous (even though the data they gathered is not), they decide to use a formula they found in an old dusty statistics textbook: expected value= [*[Cn] ·p([Cn)) d[Cn], 1 ba image 1 which in this case becomes
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