6. Create a single stack pushdown automaton that represents/accepts this regular expression. Where m>p
5. Suppose P(m,n) means “m>n”, where the universe of discourse for m and n is the set of POSITIVE integers. Find the truth value of each statement and explain your answer. NOTE: This is NOT exactly the same as the practice test. (a) (2 points) VxP(x,5) (b) (2 points) Vx3yP(x,y) (c) (2 points) ExWyP(x,y)
Write the following expression as an algebraic expression. V3 tan where x > 0 V22 +
PROBLEM 2 Consider the family of circles P = {C, TER>0}, where Cr = {(x, y) R2 | x2 + y2 = p2} is a circle of radius r > 0. Prove that P is a partition of R2. State an equivalence relation induced by this partition. Hint: What is a property that is True for all points in a fixed circle?
3. Let T = {< M > | m accepts w" when it accepts w. }. Show T is undecidable.
estimation problems . Xi, X2,..., Xn is a random sample from the common p where α > 1, We want to estimate α and β.
Question 12: Let X and Y have the joint probability density function Find P(X>Y), P(X Y <1), and P(X < 0.5)
Please answer the Stochastic Calculus in Finance question 12 and write legibly 12. Let p and q be constants with p > 0, and let zi and z2 be extended numbers. Verify that /2p where Φ(00) :--1 and Φ(-oo) :--0.
number 2 only please, could not take a smaller picture. 2 Find a regular grammar that generates the language • {w | We{0,1}* , [w] >= 4; w starts with 1 and ends with 10 or 01). 3 Find a regular expression that denotes the language accepted by the below finite automaton. 0 E B 0,1 1 D 0 с F
For any two numbers p and q, which of the following must be true? A. Ip+al 2 Ipl + 191 B. Ip-al s lpl - 191 C. Ip-al>o D. Ip.al 2p.q
Problem 6. (10 pts) Write down the following in the form of x(t) = A cos(2t + o), where A> 0 x(t) = sin(2t + 7) + cos2t