Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter2: Exponential, Logarithmic, And Trigonometric Functions
Section2.2: Logarithmic Functions
Problem 83E: Find the value of the index of diversity for populations with n species and 1n of each if...
Related questions
Question
![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] ≈~¯](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F67f82b89-727a-4a3d-8de6-b87088ff0cfe%2Fbdafd70b-33ce-4c10-a65e-30b7936fa3db%2Fhv2v6pf_processed.png&w=3840&q=75)
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F67f82b89-727a-4a3d-8de6-b87088ff0cfe%2Fbdafd70b-33ce-4c10-a65e-30b7936fa3db%2F0dl3r8_processed.png&w=3840&q=75)
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
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps
Recommended textbooks for you
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning