Natural definition for variance?

In summary, variance in natural science refers to the degree of variation or diversity within a population or ecosystem and is calculated by finding the average of the squared differences between data points and the mean. It is used to measure and track changes in a system and is closely related to standard deviation. Variance can also be used to compare different populations or ecosystems, but context and other factors should be taken into consideration when interpreting the values.
  • #1
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Homework Statement



I'm trying to find a natural definition for V[X|Y], but I'm not sure what a natural definition is. Any help?
 
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  • #2
This already has a definition. It's the second moment of X where you integrate against the pdf condition on Y. I guess I'm confused about your question.
 
  • #3
Actually I'm assuming that you're asking about V[X|Y = y] which is just a deterministic value. The way you wrote it V[X|Y] would actually be a random variable itself. Look at the second bullet here:

http://en.wikipedia.org/wiki/Conditional_expectation#Discussion
 

Related to Natural definition for variance?

1. What is the definition of variance in natural science?

Variance in natural science refers to the degree of variation or diversity within a population or ecosystem. It can be used to measure the spread of a set of data points and can provide insight into the overall health and stability of a system.

2. How is variance calculated in natural science?

Variance is typically calculated by taking the average of the squared differences between each data point and the mean of the data set. This value is then used to measure the overall variability within the data set.

3. What is the purpose of using variance in natural science?

Variance is often used in natural science to measure and understand the level of diversity within a population or ecosystem. It can also be used to track changes and fluctuations in a system over time.

4. How is variance related to standard deviation in natural science?

Variance and standard deviation are closely related in natural science, as standard deviation is simply the square root of the variance. Both measures provide insight into the spread and variability of a data set.

5. Can variance be used to compare different populations or ecosystems?

Yes, variance can be used to compare different populations or ecosystems. A higher variance indicates a greater degree of diversity within a system, while a lower variance suggests a more uniform distribution. However, it is important to consider the context and other factors when interpreting and comparing variance values.

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