Expected value from a density function

Thread starter mind0nmath
Start date Mar 19, 2008
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Density Density function Expected value Function Value

In summary, the expected value from a density function is a measure of central tendency and represents the average value of a probability distribution. It is calculated by multiplying each possible value by its corresponding probability and summing them together. The expected value is important in statistics as it summarizes the entire distribution and allows for predictions and decisions to be made. It is often used interchangeably with the mean of a density function but may differ for skewed distributions.

Mar 19, 2008

mind0nmath

Hey,
I know how to find the expected value from the density function when it is in the form:
|

fy =

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Mar 19, 2008

mathman

Science Advisor

mind0nmath said:

Hey,
I know how to find the expected value from the density function when it is in the form:
|

fy =

It looks like your question is unfinished.

What is the expected value from a density function?

The expected value from a density function is a measure of the central tendency of a probability distribution. It represents the average value that would be obtained from repeatedly sampling from a population and taking the average of the sample values.

How is the expected value calculated from a density function?

The expected value is calculated by multiplying each possible value by its corresponding probability and then summing all of these products together. This can be represented mathematically as ∑xP(x), where x is the possible value and P(x) is the probability of obtaining that value.

Why is the expected value important in statistics?

The expected value is important in statistics because it provides a single value that summarizes the entire probability distribution. This allows us to make predictions and decisions based on this value and understand the overall behavior of the distribution.

What is the relationship between the expected value and the mean of a density function?

The expected value and the mean of a density function are often used interchangeably, as they both represent the same concept of the average value of a probability distribution. However, the mean is more commonly used to refer to the expected value of a dataset, while the expected value is used to refer to a theoretical probability distribution.

How does the expected value change with different density functions?

The expected value can vary depending on the shape and parameters of a density function. Certain distributions, such as the normal distribution, have a symmetrical shape and the expected value is equal to the mean. However, for skewed or non-symmetrical distributions, the expected value may differ from the mean and may not accurately represent the central tendency of the distribution.