Find the variance of f(x) = 1/4 for -2<x<2

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In summary, the conversation discusses finding the variance for a given function. The expected value is found by integrating the original function from -2 to 2. To find the variance, the formula used is 1/4 * ∫(x-1)^2 dx with the limits -2 to 2. However, the correct answer is obtained by multiplying through by 1/4, not by integrating the probability density function. The mistake made is forgetting to square x and divide by 2.
  • #1
kuahji
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find the variance for f(x)= 1/4 for -2<x<2 & 0 elsewhere

The first thing I did was find the expected value, which was 1 (just integrated the original function from -2 to 2). Then I set up the next part as

[tex]\int (x-1)^2 (1/4) dx[/tex] with the limits -2 to 2

So it became
1/4[tex]\int x^2-2x+1 dx[/tex]
1/4(8/3-4+2)-1/4(-8/3+4-) =1/3
However, the book has the answer 4/3, which is what you get if you don't multiply through by 1/4. Is this a conceptual error on my part, or a book error? Usually it ends up being me who is wrong :(.
 
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  • #2
Sorry, but it is you. Your "conceptual error" is in the formula for the mean.

Integrating any probability density will give you 1- that's not the "mean", it is the total probability that the result is somewhere in that interval which is, by definition, 1. The mean is the integral of x times the probility density function. Here, that is
[itex]\int_{-2}^2 x(1/4) dx[/itex].
 
  • #3
Oops. Nevermind, it is my mistake. Forgot to square the x & divide by two. >.<
 
Last edited:

Related to Find the variance of f(x) = 1/4 for -2<x<2

What is the formula for calculating variance?

The formula for calculating variance is:
Variance = ∑ (x - x̄)^2 / n
Where x is each data point, x̄ is the mean of the data, and n is the total number of data points.

How do you find the mean for a given data set?

To find the mean for a given data set, add all the data points together and divide the sum by the total number of data points. In this case, the mean would be 0 since there are an equal number of data points above and below 0.

What is the range of the given function f(x) = 1/4 for -2

The range of the given function is [0, 0.25]. This means that the function can only output values between 0 and 0.25, inclusive.

How do you interpret the variance of a function?

The variance of a function measures how spread out the data points are from the mean. A higher variance indicates that the data points are more spread out, while a lower variance indicates that the data points are closer to the mean.

What is the significance of the given function having a variance of 0?

A variance of 0 for the given function indicates that all the data points are the same value, in this case, 1/4. This means that there is no variation or spread in the data set, and the function is a constant.

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