3) Let N- 11,2,3,... and Nx N -(m,n) | m,n E N. Consider f NxN-N given by f(1,2)-3 | f(2,2)-6 | f...
Iculate the probability of the foltowing events G first digit 1, 2, or 3 P(F) P(G) | F-sum of digits-4 P(F and G) P(F given G) P(F and G)/P(G) 2 Dice Sample Space 1,6 2,6 3,6 1,5 1,1 2,1 3,1 4,1 5,1 1,2 2,2 3,2 4,2 5,2 6,2 1,3 2,3 3,3 4,3 5,3 6,3 1,4 2,4 3,4 4,4 5,4 6,4 2,5 3,5 4,5 4,6 5,5 5,6 6,5 6,6 6,1 25/2018 HW 2- Probability 1
4.8.147 :3 Que Consider the population described by the probability distribution shown below. The random variable is observed twice with independent observations. | X p(x) e Sample | 1,1 1,2 1,3 1,4 2,1 2,2 2,3 2,4 Full data set e 0.2 Probability 0.04 0.04 0.06 0.06 0.04 0.04 0.06 0.06 0.2 3 0.3 Sample 3,1 3,2 3,3 3,4 4,1 4,2 4,3 4,4 4 0.3 Probability 0.06 0.06 0.09 0.09 0.06 0.06 0.09 0.09 ON a. Complete the sampling distribution table....
Let G be a graph of n nodes {1, 2, 3, ... , n}. For each permutation f of the nodes of G, we can have an induced weighting of G: the induced weight of each edge (x,y) is |f(x)-f(y)|. The total induced weight of G is the sum of the induced weights of its edges. Note that you can think of f as a relabeling of the nodes of G, where f(x) is the new label of node x,...
(1,3), с %3D (2,1), d (3,4) (1,2), b (4,2), f (5,3) and (5,5). Let 5. Let a = е 3 - {a, b, c, d, e, f, g} be the set of these 7 points. We define the following partial order on S: We have (r, y)(', y) iff x< x and y < / Draw the Hasse diagram of S S 6. We consider the same partial order as in Problem 5, but it is now defined on R2....
Consider the series following series of functions ' sin(nx) 3 n-1 a) Show that the series is absolutely and uniformly convergent on the real axis. Let f be its summation function n sin(nx) b) Show that f E C(R) and that 1 cos(nx) f'(x)= 2-1 c) Show that 「 f#072821) f(x)dx = k=0 Consider the series following series of functions ' sin(nx) 3 n-1 a) Show that the series is absolutely and uniformly convergent on the real axis. Let f...
3. Suppose that (M, ρ) is a compact metric space and f : (M, p)-+ (M,p) is a function such that (Vz, y E M) ρ (z, y) ρ (f (x), f (y)). a. Let x E (M, ρ) and consider the sequence of points {f(n) (X)}n 1 . (Remember: fn) denotes the composition of f with itself, n times, so for each n, f+() rn, k E N) such that ρ (f(m) (x) ,f(n +k) (r)) < ε ....
6. (5 pts) [MATH 4620] Use a rational function r(r) for Padé approximations of f(x)= x sinx with degrees m Compare the result at xi = 0.1 i, for i n = 3 = 1,2, 3 ,4,5, with the actual values f(xi ). 6. (5 pts) [MATH 4620] Use a rational function r(r) for Padé approximations of f(x)= x sinx with degrees m Compare the result at xi = 0.1 i, for i n = 3 = 1,2, 3 ,4,5,...
Consider the vector field: f (x, y)= «M(x, y), N(x, y)= v promet Let C be any simple, positively oriented, closed curve that encloses the origin. Show that: F. do 21. We will solve this problem by completing the following steps: STEP 1 Let C be a positively oriented circle of radius r with the center at the origin. Letr be so small that the circle Člies within the region enclosed by the curve C(see figure below) Compute the integral...
Battery Identical Lightbulbs Initially, made of tungsten which has n-6e+28 e/m 3 and u-0.0018 (m/s)/(N/C). The radius of the filament is 4.1e-06 m. The capacitance of the capacitor is 0.8 F. The total length of the connecting wires is 9 cm. Before you answer the questions below, write down two correct Δν round trip (energy conservation) equations for this circuit. The equations should be general (that is, correct for all times after t-0 and not only applicable for a specific...
Help with adjusting entries. M N O А B C D E F H K L 1 (LO 2, 3) The Blue Thumb Lawn Care Company began operations on April 1. At April 30, the trial balance shows the following balances for selected accounts. 2 3 Prepaid Insurance 3,600 4 Equipment 28,000 5 Notes Payable 20,000 6 Unearned Service Revenue 4,200 7 Service Revenue 1,800 8 9 Analysis reveals the following additional data. 10 1.Prepaid insurance is the cost of...