5. [20+5+5] In the regression modely, x,B+ s, pe,+u, ,where I ρ k l and , , let ε, follow an autoregressive (AR) process u' ~ID(Qơ:) , t-l, 2, ,n . <l and u, - Derive the variance-covarian...
3. Let U-Bt- tB be Brownian bridge on [0, 1], where {BiJosesi is a Brownian process (i) Show E(Ut0 (ii) Show Cov(U,, Ut) s(1- t) for 0 s ts1. (ii) Let Xg(t)B Find functions g and h such that X, has the same covariance as a Brownian bridge.
3. Let U-Bt- tB be Brownian bridge on [0, 1], where {BiJosesi is a Brownian process (i) Show E(Ut0 (ii) Show Cov(U,, Ut) s(1- t) for 0 s ts1. (ii) Let Xg(t)B...
QUESTION4 (a) Let e be a zero-mean, unit-variance white noise process. Consider a process that begins at time t = 0 and is defined recursively as follows. Let Y0 = ceo and Y1-CgY0-ei. Then let Y,-φ1Yt-it wt-1-et for t > ï as in an AR(2) process. Show that the process mean, E(Y.), is zero. (b) Suppose that (a is generated according to }.-10 e,-tet-+扣-1 with e,-N(0.) 0 Find the mean and covariance functions for (Y). Is (Y) stationary? Justify your...
4) Let Xi , X2, . . . , xn i id N(μ, σ 2) RVs. Consider the problem of testing Ho : μ- 0 against H1: μ > 0. (a) It suffices to restrict attention to sufficient statistic (U, v), where U X and V S2. Show that the problem of testing Ho is invariant under g {{a, 1), a e R} and a maximal invariant is T = U/-/ V. (b) Show.that the distribution of T has MLR,...
4. (a) Let Xi,X ,x, be n observations from an N(u2) distribution, and define the estimators (i) Determine whether T and T2 are unbiased estimators of u. 4 points (ii) Compute the variances Var(Ti), and Var(T2). Which is the better estimator T or T2 -and why? [2 points] Determine the maximum likelihood estimator of μ. (iii) [5 points) (b) A manufacturer is testing the performance of two products, A and B. At each of 20 field sites, product A and...
1. Let X be an iid sample of size n from a continuous distribution with mean /i, variance a2 and such that Xi e [0, 1] for all i e {1,...,n}. Let X = average. For a E (0,1), we wish to obtain a number q > 0 such that: (1/n) Xi be the sample Р(X € |и — 9. и + q) predict with probability approximately In other words, we wish to sample of size n, the average X...
T F 5, Σ = {a,b), L = { s: s = anbm, nzn, m20, Isl s IP(Σ)13. (Th not longer than the number of elements in the power set of 2.) The re language pumping theorem could show that L RLs. T F 6. An NDFSM that recognizes a language L may have computation branc at is, s e L iff s is it accepts a string w L. 7. ISI = Ko, where S is a set. Ir(s)l...
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Exercise 25: Let f 0,R be defined by f(x)-1/n, m, with m,nENand n is the minimal n such that m/n a) Show that L(f, P)0 for all partitions P of [0, 1] b) Let mE N. Show that the cardinality of the set A bounded by m(m1)/2. e [0, 1]: f(x) > 1/m) is c) Given m E N construct a partition P such that U(f, Pm)2/m. d) Show that f is integrable and compute Jo...
ONLY NEED H, I, J, K, L, M
1. (65 points: 5 points each) For each situation below, what is the most appropriate probability model for the random variable X? (no n a) Let X - how many customers will buy a sofa tomorrow at Wolf's furniture store. b) In a program that provides free home inspections for seniors, let X- how many homes eed to specify parameter values) are inspected before one needs a new roof. c) Let X...
please show work ive attatched the answers
l T-Mobile LTE 11:23 AM ร 49%! × HW10-CHAP 8 N 9 STA 250.pdf 2 of 5 SHORT ANSWER. Write the word er phrase that best completes each statenest or answers the question S A sample of 36 students anroill in a program that claims to impeove scoees on the quantitative reasoning portion of the Graduate Record Examination (GRE). The participants take a mock GRE test before the program begins and again at...