2.3. The power output P in MW from a wind farm is a function P(w) = 3w² of the wind speed w in m/a. Suppose that the wind speed is uniformly distributed on the interval [5, 15). (a) What is the probability that the wind speed is at least 10 m/.? (b) What is the probability that the power output is at least 300 MW? (c) What is the expected power output E[P]

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
icon
Related questions
Question
2.3. The power output P in MW from a wind farm is a function P(w) = 3w² of the wind speed w in
m/s. Suppose that the wind speed is uniformly distributed on the interval [5, 15].
%3D
(a) What is the probability that the wind speed is at least 10m/?
(b) What is the probability that the power output is at least 300 MW?
(c) What is the expected power output E[P]
(d) Suppose now that the wind turbines adjust for high wind speeds to reduce loading. This
means that the wind farm has a maximum power output of 300 MW, so:
3w? w < 10
S(t) =
300 w > 10
What is the expected power output E[P] of the wind farm?
Transcribed Image Text:2.3. The power output P in MW from a wind farm is a function P(w) = 3w² of the wind speed w in m/s. Suppose that the wind speed is uniformly distributed on the interval [5, 15]. %3D (a) What is the probability that the wind speed is at least 10m/? (b) What is the probability that the power output is at least 300 MW? (c) What is the expected power output E[P] (d) Suppose now that the wind turbines adjust for high wind speeds to reduce loading. This means that the wind farm has a maximum power output of 300 MW, so: 3w? w < 10 S(t) = 300 w > 10 What is the expected power output E[P] of the wind farm?
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps

Blurred answer
Similar questions
Recommended textbooks for you
A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability
A First Course in Probability
Probability
ISBN:
9780321794772
Author:
Sheldon Ross
Publisher:
PEARSON