show that u(n) = summation k=-inf to n delta(k) =summation k=0 to infinity delta(n-k)

prove that {1/n} n=1 to inf is not compact in R with usual metric. suppose use the adjoint point {0} to {1/n} n=1 to inf

Consider the simplified classical normal linear regression problem written in matrix notation:y = Xβ + u, u ∼ N (0, σ 2 I n ), β ∈ R K , σ > 0

let f:X -> (0,inf) be a continuous function on a compact space X. show that there exits an ε >0 such that f(x)>=ε for all x element of X

Suppose that \left\{ a_{0},a_{1},a_{2},\cdots ,a_{n}\right\} are knownparameters and x is an unknown variable. The equation \sum_{k=0}^{n}a_{k}x^{k}=0 has

Show that the equation (k + 1)x2 − 2x − k = 0 has a solution for all values of k