1.(a) Find S6,1, S5,1, S5,2 and Se,6-
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A: (As per bartleby guideline, For more than one question asked only one will be solved. Please upload…
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Q: 5 5 -2 6 det -1 0 10 = 47 -3 5 5 -2 6 det-1 0 10 = - 165 7 -3 5 5 -2 6 O det -1 0 10 = 0 7 -3 5
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Q: 1. If = (1.0.-3) and i = (6,-3,-4) compute ixw.
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- Assume the discrete population model: Nt+1=bNt, t=0,1,2,... Assume that the population increases by 2% each generation. a) Determine b b) Find the size of the puopulation at generation 10 when N0=20 c) After how many generations will the population have doubled?Let U1, U2, ... be i.i.d. Uni(0, 1) random variables. - log U; is distributed as exp(1). (2) Find the limit of the random sequence (U1U2 · · Un)"", as n → o. (3) Describe what happens to the sequence of random variables eVn (U¡U2 · · · Un)'/v™, (1) Show that X; as n → ∞?Suppose X1,…,Xn,…are identically distributed with mean E(X1)=μ<∞ and Var(X1)=σ2<∞. In addition, we assume that Cov(Xk,Xk+1)=0 for k=1,2,… but Cov(Xk,Xj)=0 whenever ∣k−j∣≥2. (a) Find the limiting distribution ofXˉn=n−1i=1∑nXiasn→∞. (b) Find the limiting distribution of Zn=∑nnXin+∑n=1nXiX,eias n→∞. (c) LetY1,Y2… be i.i.d random variables with mean 0 and variance 1 . Additionally, letXk=Yk+Yk+1 for ,k≥1. Find the limiting distribution of Xˉn⋅
- The table shows data from a stadium concession stand, representing average temperature (x) in degrees Fahrenheit and the number of popsicles sold (y). A 4-column graph with 6 rows. Column 1 is labeled x with entries 65, 72, 85, 88, 92, sigma-summation x = 402. Column 2 is labeled y with entries 22, 25, 52, 65, 78, sigma-summation y = 242. Column 3 is labeled x squared with entries 4,225, 5,184, 7,225, 7,744, 8,464, sigma-summation x squared = 32,842. Column 4 is labeled x y with entries 1,430, 1,800, 4,420, 5,720, 7,176, sigma-summation x y = 20,546. Which regression equation correctly models the data? y = 0.60x – 17 y = 0.60x – 0.16 y = 2.09x – 114 y = 2.09x – 120Let pk(n) denote the number of partitions of the integer n into atmost k parts. Find the generating function summation pk(n)x^n. Let Dn be as in Example 10. Find a Hamiltonian circuit inCay({(r, 0), (f, 0), (e, 1)}:D4 ⨁ Z5).Does your circuit generalize to the case Dn ⨁ Zn+1 for all n ≥ 4?