Below is the formal definition of a DFA: M = (Q, Σ, δ, q0, F), where: Q = {q0, q1, q2} Σ = {a, b} δ(q0, a) = q1 δ(q0, b) = q0 δ(q1, a) = q2 δ(q1, b) = q0 δ(q2, a) = q2 δ(q2, b) = q2 F = {q2} (2.a) Draw a transition diagram for the DFA M. (2.b) Describe the language accepted by M, either in your own words or using set notation.

H1. Compute the value of an European Call option at time 0 for the following parameters: strike, K = 120, maturity 1 year, σ = 0.15, S0 = 120 and interest rate, r = 0.02: (a) by implementing, using Python, R, C++ or Matlab, a binomial model where n = 100, 1000, or 10000. For each value of n compute the error (difference between option value obtained using the B-S model and the one from the binomial model). Compute ∆0.

2. Consider two strings X and Y as given below; X= {a, c, b, a, e, d} Y = {a, b, c, a, d, f} Construct a LCS table and find out the length of the longest common subsequence (LCS) and the LCS itself, using Dynamic Programming Algorithm.

Complete the tables for dynamic programming for the Longest Common Sub-sequence (LCS) Problem on X = CGAT AC and Y = ACGCT AC. Let c(i, j) represent the length of LCS(X;,Y;), where X; the first i letters of X and Y; = (y1, Y2, . .. , Y;) contains the first j letters of Y. (x1, x2, . .. , xi) contains Fill in the missing values of the entries. A A 1 1 1 1 G 2 2 2 A A In the following, each entry b(i, j) E {†,\,+} represents the direction of recursion for c(i, j). Specifically,b(i, j) =K if x; = Yj; otherwise, b(i, j) =† if c(i – 1, j) > c(i, j– 1); b(i, j) =+- if c(i – 1, j) < c(i, j – 1). Fill in the missing values of the entries. b A G A C C What is the LCS of X and Y? Ulo - uloKE O o o o o o o O O o oo o GATAU

Follow the given steps to convert an NFA to its equivalent DFA:  Suppose we are given the following NFA over the alphabet {a, b}: Compute the lambda-closure for each of the following states:                  λ(0) =                  λ(1) =                  λ(2) =                  λ(3) =

What Language is accepted by the pda given below?M={(q1, q2, q3, q4, q5),(a,b),(0,1,z), ?, q0, z, (q5)}?(q0, b, z) = (q1, 1z)?(q1, b, 1) = (q1, 11)?(q2, a, 1) = (q3, λ)?(q3, a, 1) = (q4, λ)?(q4, a, z) = (q4, z), (q5, z)

I'm facing significant difficulties with section 2.5 part B. Despite making several attempts, I'm unable to arrive at the correct solution. In order to address part B of section 2.5, I require the question from section 2.4. The problem involves pushdown automata, and it would greatly aid me if you could provide a visual representation demonstrating the steps you took to solve it. Attached is my incorrect answer for your review. Could you please assist me in identifying the errors in my approach? My focus is specifically on rectifying the issue with question 2.5 part B. question for 2.5 2.5 Give informal descriptions and state diagrams of pushdown automata for the languages in Exercise 2.4. question for 2.4 that you will need for 2.5 2.4 Give context-free grammars that generate the following languages. In all parts, the alphabet Σ is {0,1}. b. {w| w starts and ends with the same symbol}

Discrete Structure

Write python Code for classifier QMi=1 p(yi|X, α)