Wind engineers have found that wind speed u (in meters per second) at a given location follows a Rayleigh distribution of the type 1 W(v) = 32 ve This means that at a given moment in time, the probability that u lies between a and b is equal to the shaded area in the following figure. W 0.1 -²164 0.05- graph of W(v) b 20 -v (m/s) (a) Find the probability that v = [0, b]. (Express numbers in exact form. Use symbolic notation and fractions where needed. Give your answer in terms of b.)
Wind engineers have found that wind speed u (in meters per second) at a given location follows a Rayleigh distribution of the type 1 W(v) = 32 ve This means that at a given moment in time, the probability that u lies between a and b is equal to the shaded area in the following figure. W 0.1 -²164 0.05- graph of W(v) b 20 -v (m/s) (a) Find the probability that v = [0, b]. (Express numbers in exact form. Use symbolic notation and fractions where needed. Give your answer in terms of b.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Wind engineers have found that wind speed u (in meters per second) at a given location follows a Rayleigh distribution of
the type
W(v) = 32ve-1²/164
This means that at a given moment in time, the probability that v lies between a and b is equal to the shaded area in the
following figure.
W
0.1-
0.05 +
a
graph of W(v)
b
20
→v (m/s)
(a) Find the probability that v € [0, b].
(Express numbers in exact form. Use symbolic notation and fractions where needed. Give your answer in terms of b.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbe70156d-6630-4fa1-bd10-160edc6ae6ae%2Fe84d1999-fe97-47cb-8378-b775cc688a72%2Fyt3tg1_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Wind engineers have found that wind speed u (in meters per second) at a given location follows a Rayleigh distribution of
the type
W(v) = 32ve-1²/164
This means that at a given moment in time, the probability that v lies between a and b is equal to the shaded area in the
following figure.
W
0.1-
0.05 +
a
graph of W(v)
b
20
→v (m/s)
(a) Find the probability that v € [0, b].
(Express numbers in exact form. Use symbolic notation and fractions where needed. Give your answer in terms of b.)
![probability that v = [0, b]:
(b) Calculate the probability that v € [1,5].
(Express numbers in exact form. Use symbolic notation and fractions where needed.)
probability that v € [1,5]:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbe70156d-6630-4fa1-bd10-160edc6ae6ae%2Fe84d1999-fe97-47cb-8378-b775cc688a72%2F6sfpugr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:probability that v = [0, b]:
(b) Calculate the probability that v € [1,5].
(Express numbers in exact form. Use symbolic notation and fractions where needed.)
probability that v € [1,5]:
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