this question deals with the “Laguerre Polynomials,” which are orthogonal with respect to the inner product hf, gi = Z ∞ 0 f(x)g(x) e −x dx. Use the fact that ∀ integers p, q ≥ 0 hx p , xq i = (p + q)! (“p plus q factorial”), to derive the first 4 (order 0, 1, 2, 3) orthonormal Laguerre Polynomials starting from elements of the standard polynomial basis {1, x, x2 , x3}. Let T ∈ L(C 7 ) be defined by T(z1, z2, z3, z4, z5, z6, z7) = (πz1+z2+z3+z4, πz2+z3+z4, πz3+z4, πz4, √ 7z5+z6+z7, √ 7z6+z7, √ 7z7) Let Bs(C 7 ) = {e1, e2, e3, e4, e5, e6, e7} be the standard basis of C 7 (a) (25 pts.) Find M(T, Bs(C 7(b) (25 pts.) Find the eigenvalues {λk}k=1,...,? (c) For each eigenvalue, λk: i. (30 pts.) Find the eigenspace E(λk, T) ii. (30 pts.) Find the generalized eigenspace G(λk, T)

Find the P value in a left tail T test when the test statistic (t value) is -2.345 and the sample size is 11. (Answer should be two decimals in ascending order)

Post a 200- to 400-word analysis of the similarities and differences between parametric and nonparametric tests, justifying when it is appropriate to run a nonparametric test and when it is not. Identify three parametric tests and nonparametric equivalents in your analysis.Be sure to support your postings and responses with specific references to the reading(s) and/or media segment(s) and use APA format.