random variables X and Y are related by a relation YaX+b and you had a set of observations (1.1), (2, 2).....(.)). then for every estimated values of a and b, the Sum of Squared Errors (SSE) was defined as in the following formula. SSE =(-ax-b)². P

Solve the recurrence relations shown below. a. T(n)={4T(n−1)+1if n>11if n=1T(n)={4T(n−1)+1if n>11if n=1 -- b. T(n)={3T(n/3)+4nif n>11if n=1

Logistic regression aims to train the parameters from the training set D = {(x(i),y(i)), i 1,2,...,m, y ¤ {0,1}} so that the hypothesis function h(x) = g(0¹ x) 1 (here g(z) is the logistic or sigmod function g(z) can predict the probability of a 1+ e-z new instance x being labeled as 1. Please derive the following stochastic gradient ascent update rule for a logistic regression problem. 0j = 0j + a(y(¹) — hz(x)))x; ave. =

Use & for •, v for V, > for Ɔ, and = for = What can you derive by applying De Morgan's (DM) to this formula: ~(N • E) Ɔ G (N v E) > G O (-N v -E) > G O (N & E) v G O (N & E) v G O (N v E) > G O (N & E) > G

Consider the following recurrence relation: T(0) = 2, T(1) = 5, T(n) = 27(n – 1) – T(n – 2) for n>1 Write out the first few values T(0), T(1), T(2),...,. Make a guess about the closed form of T(n) and then prove that it is a closed form for T(n) using induction.

1(a). For an M/M/1 queuing system, write your own function in R to compute andoutput the:1. long-run probability po,p1,…,pn of there being 0,..,n people in the system.2. the values L, Lq, W, Wq, and Wse. The function should return elements with the names probs (vector of po,…,pn), L, Lq, W,Wq, and Wse (does not have to be in this order) The function should take as inputs, lambda (arrival rate), mu (service rate), and n (thenumber of people to compute probabilities for 0,…,n) Note: you are to code the computations for the above on your own, so none of the functionsin the queueing package are to be used. 1(b).  Using your function from 1(a), find the values (b)-(f) in the Queuing Theory(M_M_1).

8. Solve the following recurrence relations. (16 points) a. T(n) = 4T(n-1) + 1 for n > 1; T(1) = 1; b. T(n) = T(n/2) + 3; T(1) = 1; Here you can assume that n=2k for some integer k.

Standard and Canonical Forms | Verilog | K-Map Consider the following Boolean Function: F(p,q,r) = p'q' + p'r' + qr On a separate sheet of paper complete the truth table for the function then transcribe the information requested below. Express the function in three canonical forms F(p,q,r) = F(p,q,r) = F(p,q,r) = Minimized function р q r Notation Designation F On a separate sheet of paper prepare and complete a K-Map for the function and use it to minimize the function X yz 0 1 F (p, q, r): = 00 1 mo 0 x'y'z' C r Minterm 1 1 01 C C r r 1 1 11 C C r r 1 1 10 C C r r