- #1
hellokitten
- 12
- 1
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.
Last edited:
I guess the z should be X, or 9var(x) should be 9Var(Z). Either way, what assumption does that step require?hellokitten said:Var(3x^2 +3z +1) = 9Var(x^2) +9Var(x)
haruspex said:I guess the z should be X, or 9var(x) should be 9Var(Z). Either way, what assumption does that step require?
hellokitten said:Homework Statement
Find the variance of Y=3x^2+3x+3The 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.
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.
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.
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.
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.
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.