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1. Expand the following: a) Σ ( a + b%) where i varies from 1 to n. b) ( Σ up where i varies from 1 to 3. 2a) Define the arithmetic mean, mode, and the median. MeaR b) Consider the following data on grades received by a student in a particular course Weight 25% o 30% .30 45% , Tests Grades Test145 Test 2: 50 Final Exam: 65 Compute the weighted average of grades. 3 a) In 2015, the...
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Let Xi ~ N(μ, σ?), where ơỈ are known and positive for i-1, are independent. Let /- (a) Find the mean and variance of μ. (b) Compare μ to X,-n-Σί.i Xi as an estimator of μ. , n, and Xi, X, , E-1(1/o .m be the MLE of μ.
Let Xi ~ N(μ, σ?), where ơỈ are known and positive for i-1, are independent. Let /- (a) Find the mean and variance of μ....
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4. Suppose that (Xi,K), , (XN,Yv) denotes a random sample. Let Si-a+ bXi, T, e+dy, where a, b, c and d are constants. Let X-., Σ Xi, and σ Σ (Xi-X)2, with the analogous expressions for y, ST. Let ởXY-NT Σ(Xi-X)(y-y), and...
1. A vector B = Bxi + Byj, when added to the vector C = 3.0i + 4.0j, yields a resultant vector A that is in the negative y- direction and has a magnitude which is twice that of C. Find (a) Bx and By, (b) the magnitude of B, (c) the angle between B and C. 2. John had a good long walk on Sunday morning with his dog. He started from his home walking 1.2 mile east, then...
Let Σ = {0, 1). (a) Give a recursive definition of Σ., the set of strings from the alphabet Σ. (b) Prove that for every n E N there are 2" strings of length n in '. (c) Give a recursive definition of I(s), the length of a string s E Σ For a bitstring s, let O(s) and I(s) be number of zeroes and ones, respectively, that occur in s. So for example if s = 01001, then 0(s)...
Expand the below function in terms of (1. cos i), where N is positive integer and 0 s x s L 2 2 f(x) = Determine what function this expansion of f(x) converges to on 0 x s L. Graph the function itself, as well as the two partial sums of the expansion, proving the accuracy of the expansion improves as n increases.
Assume X is a random variable following from N (μ, σ2), where σ > 0. (a) Write down the pdf of X. (b) Compute E(X2) (b) Define Y.Find the distribution of Y
Give an example of a function f: Σ* x N -> Z , where Σ = {a,b} and where N represents the non-negative integers and Z represents the integers.
Question 5 Suppose we have the following two samples , rini from No(21, Σ), Sample l: r1 1, Sample 2: T21 , . . . , z2n2 from MgWa, Σ 2). Two new = C2, + d for all 1-1,2 and j = 1, 2, . . . ,n, where C is a p x p nonsingular matrix and d is a p x 1 vector. Based on Samples and 2, the T2-statistic for testing μι μ2 is denoted as...
04) a) Prove the following relations N, a i)Σ a. =11-as, otherwise 1-a b) Find the result of the following expressions, At