Let there be the random vector Z E Rm Prove that E (||Z||*) = tr(E[ZZ"]) From the expression above, conclude that if E[Z]=0 then: E (|Iz||*) = tr(cov[Z)
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![Let there be the random vector Z E R"
Prove that E (||Z|) = tr(E[ZZ"])
From the expression above, conclude that if E[Z]=0 then:
E (|Iz||) = tr(cov[Z])](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe19f3074-96ea-43a4-ab15-b02b56bba91a%2F69311a40-3cb1-4c94-b6bb-a86461d6fdd7%2Ftxuvgyj_processed.jpeg&w=3840&q=75)
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- Consider the pdf e!/3(z) 0Plz asapSuppose that the joint density function of two random variables W₁ and W₂ is given by F (w₁, W₂) = {C(W₁ + w?), 0, 05. Assume that {X;}", for integer m, are a random sample from a Gamma(n, 1/k) distribution, where n is also an integer and x > 0. Determine the large sample approximation to the joint distribution of Vn{X;/n - k} noting any first and second moments explicitly in this distribution. Define a new vector V whose entries are Y; = E, X for j = 1,..., 4. Determine the mean and covariance of V. You may use results on the 1st and 2nd moments of the Gamma distribution from the course formula sheet on moodle without re-deriving the results, and more generally that the Ith uncentered moment of the Gamma(a, 8) distribution takes the form (for lE N): E(x'} = | -Bs dr e r(a) r(a +1) T(a)) J. r(a+ 1) r(a +1) r(a)3 lta-1 e dr 1= 1,2, 3, ... r(a+l) We recognize Ta = (a +1- 1)a-1 as the falling factorial for integer a. %3DAssume that S={O1, O2, O3, O4} and that w1 = 0.22, w2 = 0.12, w3 = 0.17, w4 = 0.49. Let E={O2, O3} and F={O3, O4}. (a) What is the probability Pr[E]? (b) What is Pr[F′]? (c) What is Pr[(E∪F)′]?Consider x1 = (I11, F12)" and x2 = (In, I2)". Let x = (x, x})T and e el IPP P Plpp P P Cov(x) = PPlp Le Pp] PPP for some pe (-1, 1). Determine the first pair of canonical variables.Recommended textbooks for youCalculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage Learning
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