2. In probability, it is common model the deviation of a day's temperature from the monthly average temperature using the Gaussian probability density function, S(t) = - This means that the probability that the day's temperature will be between t = a and t = b different from the monthly average temperature is given by the area under the graph of y = f(t) between t = a and t = b. A related function is F(z) = *° dt, 120. This function gives the probability that the day's temperature is between t = -z and t = 1 different from the monthly average temperature. For example, F(1) × 0.36 indicates that there's roughly a 36% chance that the day's temperature will be within 1 degree (between 1 degree less and 1 degree more) of the monthly average. (a) Find a power series representation of F(x) (write down the power series using sigma notation). (b) Use your answer to (a) to find a series equal to the probability that the day's temperature will be within 2 degrees of the monthly average. (c) Now approximate your answer to (b) to within 0.001 of the actual value. Make sure you justify that the error in your approximation is no greater than 0.001.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
2. In probability, it is common to model the deviation of a day's temperature from the monthly
average temperature using the Gaussian probability density function,
f(t) =
This means that the probability that the day's temperature will be between t = a and t = b
different from the monthly average temperature is given by the area under the graph of
y = f(t) between t = a and t = b.
A related function is
2
F(1) =
e2/9 dt, r20.
This function gives the probability that the day's temperature is between t = -x and t = r
different from the monthly average temperature. For example, F(1) = (0.36 indicates that
there's roughly a 36% chance that the day's temperature will be within 1 degree (between 1
degree less and 1 degree more) of the monthly average.
1
(a) Find a power series representation of F(r) (write down the power series using sigma
notation).
(b) Use your answer to (a) to find a series equal to the probability that the day's temperature
will be within 2 degrees of the monthly average.
(c) Now approximate your answer to (b) to within 0.001 of the actual value. Make sure you
justify that the error in your approximation is no greater than 0.001.
Transcribed Image Text:2. In probability, it is common to model the deviation of a day's temperature from the monthly average temperature using the Gaussian probability density function, f(t) = This means that the probability that the day's temperature will be between t = a and t = b different from the monthly average temperature is given by the area under the graph of y = f(t) between t = a and t = b. A related function is 2 F(1) = e2/9 dt, r20. This function gives the probability that the day's temperature is between t = -x and t = r different from the monthly average temperature. For example, F(1) = (0.36 indicates that there's roughly a 36% chance that the day's temperature will be within 1 degree (between 1 degree less and 1 degree more) of the monthly average. 1 (a) Find a power series representation of F(r) (write down the power series using sigma notation). (b) Use your answer to (a) to find a series equal to the probability that the day's temperature will be within 2 degrees of the monthly average. (c) Now approximate your answer to (b) to within 0.001 of the actual value. Make sure you justify that the error in your approximation is no greater than 0.001.
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
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 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…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
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
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman