Tagged Questions
0
votes
1answer
119 views
Show that $E(XY) = σ_{XY} + μ_Xμ_Y$?
Let X and Y be two random variables with means $μ_X$ and $μ_Y$ , variances $σ^2_Y$, $σ^2_X$ and covariance $σ_{XY}$ . Show that $E(XY) = σ_{XY} + μ_Xμ_Y$?
I tried the Covariance formula with:
...
0
votes
0answers
54 views
Estimation of max likelihood sample mean and sample covariance
How do I estimate the maximum likelihood sample mean and sample covariance of the data set consisting of
N = 100 2-dimensional samples x = (x1 , x2 )T ∈ R2 drawn from a 2-dimensional Gaussian ...
0
votes
2answers
179 views
Need help to understand the meaning of this formula
I need help to understand the meaning of the following formula:
$$\sum_{i=1}^n\sum_{j\neq i,j=1}^n(x_i-\mu_i)(x_j-\mu_j)c_{ij}$$
where C is positive semidefinite matrix, $\mu_i$ is the mean of ...
5
votes
2answers
235 views
One component in PCA is always the mean vector in two-dimensions but not three
I've been testing PCA via SVD to decompose a simple time series data matrix, $X$. I have two signals $x_1(t)$ and $x_2(t)$ in a data matrix where $M$ rows represents each timepoint sample and each ...
