Probability density functions

In summary, the data in the graph follows a Gaussian distribution. The way to interpret it is to look at the number of fibres in each category and then express it as a proportion of the total number of fibres.
  • #1
jamie516
17
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This could go in the homework section I suppose, but I couldn't follow the guidelines, so I'll try asking it here.

The attached image is a probability distribution for measured fibre angles from a spray up carbon fibre process. This is in a report that I need to explain. To get the probability distributions on the Y axis, would one just add up all the fibres, and divide that total by the number between a given orientation?
 

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  • #2
jamie516 said:
This could go in the homework section I suppose, but I couldn't follow the guidelines, so I'll try asking it here.

The attached image is a probability distribution for measured fibre angles from a spray up carbon fibre process. This is in a report that I need to explain. To get the probability distributions on the Y axis, would one just add up all the fibres, and divide that total by the number between a given orientation?

I'm not sure what you are asking. The data appears to follow a Gaussian Distribution (i.e. Normal Distribution). The way to interpret the graph is like this: For the 6k 115mm fibers, there is a 0.29 probability that the in-plane fiber orientation is approximately 0.0 radians.

CS
 
  • #3
I'm asking how would generate the probabilities on the Y-axis?
 
  • #4
jamie516 said:
I'm asking how would generate the probabilities on the Y-axis?

Your graph shows the y-axis as "probability" already. So there's nothing to generate.

CS
 
  • #5
I know it does, what I'm asking is how was it obtained in the first place? Would you just add up the number of fibres between a certain angle and then divide by the total number of fibres? And that gives probability?
 
  • #6
It's generated by looking at all the fibres, putting each one into a category (of orientation), and counting up how many fibres are in each category; then expressing that number as a proportion of the total number of fibres.

This should have been posted in homework help.
 
  • #7
Yes, that's what I thought, thanks for your help, maybe it can be moved?
 

What is a probability density function?

A probability density function (PDF) is a mathematical function that describes the probability distribution of a continuous random variable. It is used to determine the likelihood of a random variable falling within a specific range of values.

How is a probability density function different from a probability distribution?

A probability distribution is a set of all possible outcomes of an experiment and their corresponding probabilities. A probability density function, on the other hand, is a mathematical representation of this probability distribution in the form of a curve or function.

What is the area under a probability density function?

The area under a probability density function between two points represents the probability of the random variable falling within that range. This is because the total area under the curve is always equal to 1.

What is the relationship between a probability density function and a cumulative distribution function?

A cumulative distribution function (CDF) is the integral of a probability density function. It gives the probability of a random variable being less than or equal to a specific value. In other words, the CDF is the accumulation of probabilities from the PDF.

How do you use a probability density function in real-world applications?

A probability density function is used in a variety of fields, including statistics, physics, and economics. It is used to model and predict the likelihood of certain events, such as stock prices, weather patterns, or disease outbreaks. It is also used in decision-making processes, such as risk assessment and optimization.

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