4) For two events A and B you are given that: for some p,q,r, s є Į0, 1]. Which conditions should be satisfied by p,q, r, s?
Two events, A and B, occur in the frame S at spacetime 4-vector coordinates (0;500,10,10) and (600;2000,10,10) respectively. All coordinates are given in meters. (a) What is the spacetime interval between these events? What type of interval is it? (b) How fast must an observer be moving along the x axis for the two events to be simultaneous and what is the spatial separation between the events in this case? (c) Could event B precede event A for some observer?
Problem 11.21. For k є Z, we define Ak-{x є Z : x-51+ k for some 1 є z} (a) Prove that {Ak : k Z} partitions Z. (b) We denote by ~ the equivalence relation on Z that is obtained from the par- tition of part (a). Give as simple a description ofas possible; that is, given condition "C(x,y)" on x and y s x~y if and only if "C(x, y)" holds. Problem 11.21. For k є Z, we...
BONUS QUESTION (2 MARKS): A rational function is defined by where m, n є NU0} such that not every coefficient qi İs 0 and f(z) is not defined at the values of r for which q(r) = 0. What 'special' choice(s) of q(r) will give the result that the set of all polynomial functions, p(x) P +Pn-1-1 form a subset of the rational functions (as defined above)?
Question 4 You are given the following information on Events A, B, C, and D. P(A) = .5 P(B) = .3 P (C) = .15 P(A U D) = .7 P(A ∩ C) = 0.05 P (A │B) = 0.22 P (A ∩ D) = 0.25 Compute P(D). Compute P(A ∩ B). Compute P(A | C). Compute the probability of the complement of C. What does it mean to be mutually exclusive? Give an example of two events that are...
4. Show that the field Qlx)/(z2-3) is isomorphic to Q(V3)-(a + bV3 | a,b є Q. (Hint: Imitate the argument used in lecture to show that R[z]/(x2 1) is isomorphic to C) 4. Show that the field Qlx)/(z2-3) is isomorphic to Q(V3)-(a + bV3 | a,b є Q. (Hint: Imitate the argument used in lecture to show that R[z]/(x2 1) is isomorphic to C)
S) Suppose that A and B are mutually exclusive events for which P(A) = 0.3 and P(B) = 0.5 What is the probability that (a) either A or B occurs? (b) A occurs and B does not occur? (c) both A and B occur? 4.) A forest contains twenty elk, of which five are captured, tagged and then released. Some time later, four elk are captured from this population. What is the probability that exactly two of these are tagged?...
6. Given two mutually excdlusive events 4 and B for which PlA)-027 and P(B) 0.46, find (e) P(An B); (f) P(A'n B); (g) P(A'n B); (h) P(A'uB). (c) P(AuB); (d) P(An B); (Hint: Draw a Venn diagram and fill in the probabilities associated with the various regions.)
4. (a) Show that (b) Two events A and B are said to be conditionally independent given C if P(An BIC)P(A|C)P(BC). Prove that if A and B are conditionally independent given C, then
Question 1 Select one answer. Let A and B be two independent events. If P(A) = 0.5, what can you say about P(A | B)? Cannot find it because P(B) is not known. Cannot find it because P(A and B) is not known. Cannot find it because both P(B) and P(A and B) are not known. It is equal to 0.5. It is equal to 0.25. Question 2 Select one answer. Suppose a basketball team had a season of games...