Probability distribution function

Click For Summary
The function for hours of daylight, N(d)=12+6sin(2πd/365), indicates a sinusoidal variation throughout the year. The probability distribution function can be derived from this equation by treating the day of the year as a random variable. The average number of daylight hours over the year is calculated to be 12 hours. The expected daily energy production from the solar facility is determined to be 1,070,000 calories, while the standard deviation and variance of energy production can be calculated based on the variation in daylight hours. Understanding these calculations helps in assessing energy output and efficiency for solar facilities.
tepandey
Messages
1
Reaction score
0
The number of hours, N, of daylight at a certain location can be expressed as N(d)=12+6sin(2πd/365) where d=day of the year starting with March 21.
(a) What is the probability distribution function for hours of daylight if you assume the day of the year is a random variable?
(b) What is the average number of hours of daylight at that location over the year?
(c) If the energy production, E, of a certain solar thermal energy facility at that location is dependent upon the number of hours of daylight and is found to be E(N)=107N calories per day, f
• what is the expected daily energy production over the year from that facility?
• what is the standard deviation of the energy produced?
• what is the variance of the energy production?
 
Physics news on Phys.org
Welcome to PF;
Great question - how have you been attempting it?
 
The standard _A " operator" maps a Null Hypothesis Ho into a decision set { Do not reject:=1 and reject :=0}. In this sense ( HA)_A , makes no sense. Since H0, HA aren't exhaustive, can we find an alternative operator, _A' , so that ( H_A)_A' makes sense? Isn't Pearson Neyman related to this? Hope I'm making sense. Edit: I was motivated by a superficial similarity of the idea with double transposition of matrices M, with ## (M^{T})^{T}=M##, and just wanted to see if it made sense to talk...

Similar threads

  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 12 ·
Replies
12
Views
5K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 11 ·
Replies
11
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 3 ·
Replies
3
Views
3K
Replies
8
Views
2K