Calculating Variance for Y=3x^2+3x+3

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This assumption is necessary for the calculation to be correct.In summary, the conversation discusses finding the variance of a given expression, Y=3x^2+3x+3. The attempted solution uses the assumption that there is no covariance between X^2 and X in order to calculate the variance correctly. However, this assumption is not always true.
  • #1
hellokitten
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Homework Statement


Find the variance of Y=3x^2+3x+3

The Attempt at a Solution


Let Y = 3x^2 +3x +3

Var(Y) = Var(3x^2 +3x +3) = 9Var(x^2) +9Var(x) = 9 [E[X^4] - E[X^2]^2 +E[X^2] - E[X]^2]
This is wrong.
 
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  • #2
hellokitten said:
Var(3x^2 +3z +1) = 9Var(x^2) +9Var(x)
I guess the z should be X, or 9var(x) should be 9Var(Z). Either way, what assumption does that step require?
 
  • #3
haruspex said:
I guess the z should be X, or 9var(x) should be 9Var(Z). Either way, what assumption does that step require?

Oh. It assumes no covariance.
 
Last edited:
  • #4
hellokitten said:

Homework Statement


Find the variance of Y=3x^2+3x+3

The Attempt at a Solution


Let Y = 3x^2 +3x +3

Var(Y) = Var(3x^2 +3x +3) = 9Var(x^2) +9Var(x) = 9 [E[X^4] - E[X^2]^2 +E[X^2] - E[X]^2]
This is wrong.

You have assumed that ##\text{Cov}(X^2,X) = 0,## which is not generally true.
 

Related to Calculating Variance for Y=3x^2+3x+3

What is variance?

Variance is a statistical measure that quantifies the spread or variability of a set of data points around the mean or average value. It tells us how much the data points are different from the mean.

Why is calculating variance important?

Calculating variance is important because it helps us understand the distribution of data and how much the data points deviate from the mean. It is also used in many statistical analyses, such as hypothesis testing and regression analysis.

How do you calculate variance?

To calculate variance, you first need to find the mean of the data points. Then, for each data point, subtract the mean from it, square the result, and add all the squared values together. Finally, divide this sum by the total number of data points.

What is the formula for calculating variance?

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

What is the difference between population variance and sample variance?

Population variance is calculated using the entire population of data, while sample variance is calculated using a smaller subset of the population (a sample). Sample variance is used when we do not have access to the entire population data, and it is an estimate of the population variance.

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