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Department of Computer Science and Engineering University of Nevada, Reno Reno, NV 557 Email Qipingataolcom Website wwwcseunredu/~yanq I came to the US11 Definition of the Riemann integral 3 If P = {I1,I2,,In} is a partition of I, let Mk = sup Ik f, mk = inf Ik f These suprema and infima are welldefined, finite real numbers since f is bounded;X n) occurs when = X (n), so the MLE is b n= X ( ), the maximum value of the

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0 ' ( 2 3 4 5 4 6 7 8 9 & ' !;X n) = 1 n 1(0 X (1) X (n) ), we see that a smaller , a higher value of the likelihood function However, there is a restriction{the value of cannot be below X (n) otherwise the indicator function outputs 0 Thus, the maximum value of L( jX 1;Paulina Babiak awarded Leslie Bottorff Fellowship Event Date Leslie Bottorff Fellowship supports translating students' work into clinical applications ExifII* @ (1"2i4%CanonCanon EOS Rebel T6''Adobe Photoshop CC 18 (Windows)1901 & "'0230&'' 'B' J'R' ' 'Z'b'07''07''t,u000bjr01 z245f2

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Then we turn around and use this to show that if A and B are in l(P) then so is their intersection Proof Let A 2 P, and let SA be the set of all sets B ˆ X for which A\B is in l(P) We have already proven that SA is a {system Moreover,The information in this Current Report and the exhibit attached to this Current Report as Exhibit 991 is being furnished and shall not be deemed "filed" for purposes of Section 18 of the Securities Act of 1934 or otherwise subject to the liabilities of that Section nor shall they be deemed incorporated by reference into any filing under the Securities Act of 1933 or the Securities Act of Knowing the LUP decomposition for a matrix A A allows us to solve the linear system Ax =b A x = b by first applying P P and then using the LU solver In equations we start by taking Ax = b A x = b and multiplying both sides by P P, giving

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N i=1 (Xi −X¯)2, b0 = 1 n {n i=1 Yi −b1 n i=1 Xi} = Y¯ −b1X¯ The estimators are sometimes written as βˆ 1 and βˆ0 respectively Proof Terminology for the estimation • The estimated/fitted model is Yˆ = b0 b1X (Note that we use Yˆ, to denote the predicted/fitted value ofY for a given X) • The fitted values for the n4 Cash Flow Trends Note 11 Free Cash Flow calculation above does not include the $495 million Hunter Labs settlement Free Cash Flow is a nonGAAP metric (see reconciliation of nonGAAP Financial Measures included herein) Free Cash Flow CAGR calculation uses 01 data (01 Free Cash Flow was $228 million) 103% FCF CAGR from 0112 Weighted Average Diluted SharesB) If n>kyou can always solve AX= Y c) If n>kthe nullspace of Ahas dimension greater than zero d) If n

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L = φ(x) (78) The coefficients, Bn can be computed as follows Fix m∈ N Multiplying the above equality by sin mπx L and then integrating over 0,L, we get ZL 0 φ(x)sin mπx L dx= ZL 0 X∞ n=1 Bn sin nπx L sin mπx L dx = X∞ n=1 Bn ZL 0 sin nπx L sin mπx L dx (above we ignore the question about interchanging P∞ n=1 with RL 0N x*c 4 g 405 x a cv;% " % ( % ) ) / & , 0 % 0 % 1 2 3 4 5 4 6 7 8 9 7 ;

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M= supfjf(x) jx2a;bg (We'll assume that M > 0, since otherwise there's almost nothing to prove) For any n, any given term in the sum b a n P n i=1 f a i b a n has size at most Mb a n Choose N2N so that N>2kM(b a) Then, if n>Nwe consider U(f;D n) L (f;D n) This has nterms in it, involving the di erence between the supremum and the= 4 > 8 ?Title Author suzyroman Created Date 9/3/21 543 PM

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Maximum Likelihood Estimation Eric Zivot This version 1 Maximum Likelihood Estimation 11 The Likelihood Function Let X1,, be an iid sample with probability density function (pdf) f(xi;θ), where θis a (k× 1) vector of parameters that characterize f(xi;θ)For example, if Xi˜N(μ,σ2) then f(xi;θ)=(2πσ2)−1/2 exp(−1Xs?e?vb n 6=a < 9 b_w;=b_cv;;=gfb ?P yare quadratic surds and if a p x= b p ythen a= band x= y 23 If a;m;nare positivereal numbersanda6=1,thenlog a mn=log a mlog a n 24 If a;m;nare positive real numbers, a6=1,thenlog a m n =log a m−log a n 25 If aand mare

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