Howtosignalprocessing
- What is the expectation of a matrix?
- What is the expectation of the product of two random variables?
- Is matrix multiplication well defined?
- What is the expected value of xy?
What is the expectation of a matrix?
The expected value of a matrix is defined as the matrix of expected values. = [E(Xi,j) + E(Yi,j)] = [E(Xi,j)] + [E(Yi,j)] = E(X) + E(Y).
What is the expectation of the product of two random variables?
In general, the expected value of the product of two random variables need not be equal to the product of their expectations. However, this holds when the random variables are independent: Theorem 5 For any two independent random variables, X1 and X2, E[X1 · X2] = E[X1] · E[X2].
Is matrix multiplication well defined?
Matrix multiplication
Multiplication of two matrices is well-defined only if the number of columns of the left matrix is the same as the number of rows of the right matrix.
What is the expected value of xy?
– The expectation of the product of X and Y is the product of the individual expectations: E(XY ) = E(X)E(Y ). More generally, this product formula holds for any expectation of a function X times a function of Y .
