Let T : V → W be a linear map, and let x1,…,xm and y1,…,yn be two lists of vectors in V . Suppose that
(a) x1,…,xm generate KerT, and (b) T(y1),…,T(yn) generate W.
Show that the list x1,…,xm,y1,…,yn generates V .
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3. Let T E ACUR“). {a} Suppose n = 5 and that 8 is an eigenvalue of T whose associated eigeusparre E3 is zit-dimensional.Prove that either T — 71′ or T — Q! is invertible. (b) Suppose n = 3 and that 7 and Q are the only eigenvalues of T. Furthermore, suppose that dim(E7) =diJI1(Eg) = 1. Prove that there exists (my, .3) E R3 such that T(3:,y, z) = (fi+ 8:51 VIE + By, VE+ 83). {e} Suppose a = 2 and that T4 = —I. Give an example of such a T.
Let X and Y be independent N(0; 1) RVs. Suppose U =X+Y/root 2and U =X-Y/root2a. Compute E[U], V ar(U), E[V ], V ar(V ), E[UV ].b. Derive the joint distribution of (U; V ) by using the Jacobian matrix method.
Let us say that in an electrical company, we are studying electrical charge. The electric charge is distributed over the triangle region that we enclose with y=1+x, y=1-x, and y=0. If the charge density (we use ) is per unit area, let us find the total charge on the triangle.
Let X and Y are two random variables. The expected value of X, E(X), is 2.60, the expected value of Y, (E(Y), is 2.35, and the expected value of X*Y, E(XY), is 7.06. The covariance between X,Y , Cov(X,Y) is ? (2 d.p.)
Select one:
0.870.9513.171.161.95
Let us know the name of the country that develops small town is not big cities have been developed?
The country is China.In 1987, China introduced a three-part strategy aimed to control urban growth. First, it strictly limitedthe size of big cities (500,000 or more people). Second, it developed…
q: I need help with question 13, the picture attached, please! tell me if the question is not clear.
13. Let (X 15, X2011, 2′ = 1, . – – , n, be iid random vectors from a bivariate normal distribution with mean vector (#1, ”QT, variances of, 0% and covariance 012. (8.) Write down the likelihood function;(b) Derive the maximum likelihood estimates of the five parameters, in, pg, of, 03, 012;
Let us know if you will be posting one ten page story or several shorter stories. The stories may be from the prompts. For example, you may want to complete the story that was a re-write of a fairy tale, or the story of picking someone up hitchhiking that was from history or famous or perhaps the prompt about setting will evolve into a complete story. You’ll need to make sure these stories follow the proper format for dialogue and that you proofread your story. We are working towards having a publishable story (or stories) at the end of our class. Therefore the story must be ready to submit for publication (grammatically perfect). Do the best you can. We look forward to seeing your creativity, originality and hope you have fun writing your story. 12 point Times New Roman. Double spaced. 10 pages.
Let X1,X2,…Xn be a random sample of size n form a uniform distribution on the interval [θ1,θ2]. Let Y = min (X1,X2,…,Xn).
(a) Find the density function for Y. (Hint: find the cdf and then differentiate.)
(b) Compute the expectation of Y.
(c) Suppose θ1= 0. Use part (b) to give an unbiased estimator for θ2.
Let us begin this week by looking at the “four connectors”: Please pick one and discuss in what cases the connection is true and in what cases it would be false, and see if you can give an explanation as to why this is the case. (When two claims are connected by and, in what case is the truth value false, and why?)
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