Probability distribution function

In summary, the conversation discusses the relationship between the number of hours of daylight at a certain location and the day of the year. It also introduces a solar thermal energy facility and its energy production, which is dependent on the number of hours of daylight. The questions asked include the probability distribution function for hours of daylight as a random variable, the average number of hours of daylight over the year, the expected daily energy production from the facility, the standard deviation of energy produced, and the variance of energy production.
  • #1
tepandey
1
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?
 
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  • #2
Welcome to PF;
Great question - how have you been attempting it?
 

FAQ: Probability distribution function

What is a probability distribution function?

A probability distribution function is a mathematical function that describes the likelihood of a random variable taking on certain values within a given range. It is used to model the probabilities of different outcomes in a random experiment.

What is the difference between a probability distribution function and a probability density function?

A probability distribution function is a function that maps possible outcomes of a random variable to their corresponding probabilities, while a probability density function is a function that represents the relative likelihood of different values occurring within a continuous range of values.

How is a probability distribution function calculated?

The specific calculation of a probability distribution function depends on the type of distribution being modeled. For example, for a discrete distribution, the probability of each possible outcome is calculated and then plotted on a graph, while for a continuous distribution, the probability density function is integrated over a given range to find the probability of an event occurring within that range.

What is the importance of a probability distribution function in statistics?

Probability distribution functions are important in statistics because they allow us to make predictions and draw conclusions about the likelihood of certain outcomes in a random experiment. They also serve as the basis for many statistical tests and models.

Are there different types of probability distribution functions?

Yes, there are many different types of probability distribution functions, including the normal distribution, binomial distribution, Poisson distribution, and exponential distribution. Each type of distribution is used to model different types of data and has its own unique characteristics and properties.

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