B3. (a) The village of Sunnyridge has installed an array of 6 wind turbines. The probability of any day being insufficiently windy for the turbines to operate is found to be 0.3. The probability on any day that any individual turbine needs to be shut down for maintenance is found to be 0.1. [You may assume that all probabilities are mutually independent] A monitoring device is mounted upon one of the wind turbines. (i) What is the probability that the monitored wind turbine operates on any given day? (ii) The monitored turbine is observed to be not operating. What is the proba- bility that this turbine has been shut down for maintenance? (iii) What is the probability that more than 2 of the 6 turbines are shut down for maintenance on any particular day? (iv) What is the probability that at least 4 turbines are operating on any particular day? (b) Sunnyridge decide to additionally install a solar energy plant. From prior weather records, it is estimated that the number of hours per day of sunshine at Sunnyridge S is a random variable that obeys a probability density function 0≤s<2 ½ fs(s) = 12 s 70 2≤8<12. 0 otherwise (i) What is the probability of less than 4 hours of sunshine on any given day? (ii) Find the mean and variance of the number of hours of daylight. (iii) Find the probability of there being less than 1400 hours of sunshine in a year.
B3. (a) The village of Sunnyridge has installed an array of 6 wind turbines. The probability of any day being insufficiently windy for the turbines to operate is found to be 0.3. The probability on any day that any individual turbine needs to be shut down for maintenance is found to be 0.1. [You may assume that all probabilities are mutually independent] A monitoring device is mounted upon one of the wind turbines. (i) What is the probability that the monitored wind turbine operates on any given day? (ii) The monitored turbine is observed to be not operating. What is the proba- bility that this turbine has been shut down for maintenance? (iii) What is the probability that more than 2 of the 6 turbines are shut down for maintenance on any particular day? (iv) What is the probability that at least 4 turbines are operating on any particular day? (b) Sunnyridge decide to additionally install a solar energy plant. From prior weather records, it is estimated that the number of hours per day of sunshine at Sunnyridge S is a random variable that obeys a probability density function 0≤s<2 ½ fs(s) = 12 s 70 2≤8<12. 0 otherwise (i) What is the probability of less than 4 hours of sunshine on any given day? (ii) Find the mean and variance of the number of hours of daylight. (iii) Find the probability of there being less than 1400 hours of sunshine in a year.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![B3. (a) The village of Sunnyridge has installed an array of 6 wind turbines.
The probability of any day being insufficiently windy for the turbines to operate
is found to be 0.3.
The probability on any day that any individual turbine needs to be shut down for
maintenance is found to be 0.1.
[You may assume that all probabilities are mutually independent]
A monitoring device is mounted upon one of the wind turbines.
(i) What is the probability that the monitored wind turbine operates on any
given day?
(ii) The monitored turbine is observed to be not operating. What is the proba-
bility that this turbine has been shut down for maintenance?
(iii) What is the probability that more than 2 of the 6 turbines are shut down for
maintenance on any particular day?
(iv) What is the probability that at least 4 turbines are operating on any particular
day?
(b) Sunnyridge decide to additionally install a solar energy plant.
From prior weather records, it is estimated that the number of hours per day of
sunshine at Sunnyridge S is a random variable that obeys a probability density
function
0≤s<2
½
fs(s) =
12 s
70
2≤8<12.
0
otherwise
(i) What is the probability of less than 4 hours of sunshine on any given day?
(ii) Find the mean and variance of the number of hours of daylight.
(iii) Find the probability of there being less than 1400 hours of sunshine in a year.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fedbe235b-c463-4d5e-86ea-b00c026da828%2F0a3150b1-a576-46a3-98c6-8601ded2d8df%2Fao7bcd8_processed.png&w=3840&q=75)
Transcribed Image Text:B3. (a) The village of Sunnyridge has installed an array of 6 wind turbines.
The probability of any day being insufficiently windy for the turbines to operate
is found to be 0.3.
The probability on any day that any individual turbine needs to be shut down for
maintenance is found to be 0.1.
[You may assume that all probabilities are mutually independent]
A monitoring device is mounted upon one of the wind turbines.
(i) What is the probability that the monitored wind turbine operates on any
given day?
(ii) The monitored turbine is observed to be not operating. What is the proba-
bility that this turbine has been shut down for maintenance?
(iii) What is the probability that more than 2 of the 6 turbines are shut down for
maintenance on any particular day?
(iv) What is the probability that at least 4 turbines are operating on any particular
day?
(b) Sunnyridge decide to additionally install a solar energy plant.
From prior weather records, it is estimated that the number of hours per day of
sunshine at Sunnyridge S is a random variable that obeys a probability density
function
0≤s<2
½
fs(s) =
12 s
70
2≤8<12.
0
otherwise
(i) What is the probability of less than 4 hours of sunshine on any given day?
(ii) Find the mean and variance of the number of hours of daylight.
(iii) Find the probability of there being less than 1400 hours of sunshine in a year.
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 2 steps with 32 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman