saintman4 said:where X ~ N (μ, σ2)
I know that if X is random variable, the first central moment E(X-E(X)) = E(X-μ) is zero. But I would like to know if X and μ is vector. For example if X = [x1 x2] and μ = [μ1 μ2]. What is the value of E(X-μ)?
The formula for calculating E(X-μ) for X and μ vectors is E(X-μ) = Σ(X-μ)p(X), where X represents the vector of random variables, μ represents the mean vector, and p(X) represents the probability of each value in X.
E(X-μ) is equal to the first central moment of a distribution. This is because the first central moment represents the mean or average distance of each value from the mean of the distribution, which is exactly what E(X-μ) calculates.
A positive value of E(X-μ) indicates that the majority of values in the distribution are greater than the mean. This means that the distribution is positively skewed, with a longer tail on the right side.
E(X-μ) is highly affected by outliers in the data. Outliers are extreme values that are significantly different from the rest of the data. Since E(X-μ) calculates the mean distance of each value from the mean of the distribution, outliers can greatly impact the calculation and skew the results.
Yes, E(X-μ) can be negative. A negative value indicates that the majority of values in the distribution are less than the mean, resulting in a negatively skewed distribution with a longer tail on the left side.