- #1
vptran84
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Hi,
Can someone please please show me why Var(x) = E[ x^2] - (E[X])^2.
I just don't get it. THanks in advance.
Can someone please please show me why Var(x) = E[ x^2] - (E[X])^2.
I just don't get it. THanks in advance.
vptran84 said:yeah i got that part, similar to distributive property, but where does variance come from? Like how did they get E[x^2]-(E[X])^2 ? How did they get E[x^2] and (E[X])^2 ??
So <x> = E(x). The denominator there, [tex]\int f(x)dx[/tex], always equals 1 because f is a probability density function. The definition of an expected value is just the numerator of that fraction.SpaceTiger said:[tex]<x>=\frac{\int xf(x)dx}{\int f(x)dx}=\int xP(x)dx[/tex]
BicycleTree said:So <x> = E(x). The denominator there, [tex]\int f(x)dx[/tex], always equals 1 because f is a probability density function. The definition of an expected value is just the numerator of that fraction.
BicycleTree said:So then what is <x>?
What's the difference between a distribution function and a density function?
vptran84 said:Hi,
Can someone please please show me why Var(x) = E[ x^2] - (E[X])^2.
I just don't get it. THanks in advance.
"Var(x)" represents the variance of a random variable "x". It measures the spread or variability of the data points around the mean. "E[x^2]" represents the expected value of "x" squared, while "(E[X])^2" represents the square of the expected value of "x". Substracting the square of the mean from the expected value of the squared variable gives us the variance.
Calculating the variance allows us to quantify the variability of the data and understand how spread out the data points are from the mean. It also helps in comparing different datasets and identifying patterns or trends in the data.
The standard deviation is the square root of the variance. It measures the average distance of the data points from the mean. A higher variance indicates a larger spread of data points, resulting in a higher standard deviation.
No, the variance cannot be negative. It is always a non-negative value, as it represents the squared differences between the data points and the mean.
The variance is a critical concept in statistics and is used in various fields of research, such as economics, biology, psychology, and physics. It is used to analyze data, make predictions and in hypothesis testing. It also helps in understanding the accuracy and reliability of data and identifying outliers or unusual data points.