(a) Prove the Chernoff bound: PLY 2ESEe v20 (b) Find the tightest Chernoff bound on PLY2E for fy)
Please do both (a) and (b) and fully explain in detail. Problem 4. Chernoff bound for a Poisson random variable. Let X be a Poisson random variable with parameter λ (a) Show that for every s 20, we have (b) Assuming that k > λ, show that
MODERN EUCLIDEAN GEOMETRY AF = Fy prove that 5 A B E DIE
Problem 2 Prove the following bound known as the Chemoff bound: Let X be a random variable with moment generating function X (s) defined for s > 0, Then for any a and any s > 0, Hint: To prove the bound apply Markov's inequality with X replaced by e) Apply the се Chemoff bound in case X is a standard normal random variable and a > 0. Find the value of s >0 that gives the sharpest bound, i.e,...
Name: Question 4. Let Y be a discrete random variable with ply) given in the table below. p(y0.2 0.30.5 a) Find the cumulative distribution function (CDF)Fy) Be sue to specify the value of Fly) for all y,y b] Sketch the distribution function given in part [a]
For each C++ function below, give the tightest can asymptotic upper bound that you can determine. (a) void mochalatte(int n) { for (int i = 0: i < n: i++) { count < < "iteration;" < < i < < end1: } } (b) void nanaimobar (int n) { for (int i = 1: i < 2*n: i = 2*i) { count < < "iteration;" < < i < < end1: } } void appletart (int n) { for (int...
(4) Suppose that an → a. Prove or disprove: (a) If an is an upper bound fora set S for all n, then a is also an upper bound for S. (b) If an € (0,1) for all n, then a € (0,1). (c) If an € [0,1] for all n, then a € [0, 1]. (d) If an is rational, then a is rational.
If a statement is true, prove it. If not, give an example of why it is false. Please neatly and carefully show all necessary work. u. JUULEGADU V W le CLLIULIA LIIV LIVES CASUAL .U . 7. If PLY f(x,y) = if (x, y) + (0,0) if (x, y) = (0,0), then fr(0,0) = 1 and f,(0,0) = 0. 8. If fe and fy are both bounded in an open ball about (a,b), then f is continuous at (a,b).
A lo V20 2 0 - 1 1 1 (a) (b) Determine the singular values of A. Find the singular value decomposition of A. Your answer has to consist of three matrices U, E, V satisfying the appropriate properties and multiplied together to retrieve A.
4. For the following sets determine the least upper bound (it is not necessary to prove that it is the least upper bound): a.) M = [0; 1] [ (3; 4) b.) M = n5n + 1 4n ? 3 n 2 N o c.) M = n n + 1 2n + 13 n 2 N o d.) M = nXn i=1 9 10i n 2 N o e.) M = n xjx > 0 and x2 < 5g:...
For the series a) Find the partial sum $10. b) Find an upper and lower bound for the error Rio. =) Find an upper and lower bound for the sum s. Use the midpoint of the internal of the upper and lower bound found to get a better estimate of s. What's the maximum error for this new estimate of s?