24. Consider a system made up of two spin particles. Observer A specializes in measuring the spin components of one of the particles (S, S, and so on), while observer B measures the spin components of the other particle. Suppose the system is known to be in a spin-singlet state, that is, Stotal = 0. a. What is the probability for observer A to obtain s1 h/2 when observer B makes no measurement? Same problem for s1, = h/2. b. Observer B determines the spin of particle 2 to be in the s2, = h/2 state with certainty. What can we then conclude about the outcome of observer A's measurement if (i) A measures S1; and (ii) A measures s,? Justify your answer.

Fall23 HW3.3. Let y0nd. Exp(0.), Inv-Gamma (a, 1), for i=1,..., n. Find the empirical Bayes estimator of 0,, i 1,..., n (Note: If z~ Exp(0), then p(x)=1/0e-1/0 and if Inv-Gamma(a, 3), then p(x) = 1/{3ªT(a)}r-a-¹e-¹/³).).

You roll an 8-sided die. Let A = {4, 5, 7, 8} and B = {1, 3, 6, 7}. Find the following. S = { A' = B' = P(A') = P(B') = n(A' AND B) = n(A OR B') = P(A OR B') = Ρ(A' AND Β) - P(A | B') = %3D P(A' | B) = %3D

Bighorn sheep are beautiful wild animals found throughout the western United States. Let x be the age of a bighorn sheep (in years), and let y be the mortality rate (percent that die) for this age group. For example, x = 1, y = 14 means that 14% of the bighorn sheep between 1 and 2 years old died. A random sample of Arizona bighorn sheep gave the following information: y USE SALT 2= Σχ = 15; Σy = 88.3; Σx2 = 55; Σy2 = 1,594.89; Σxy = 275.8 (a) Find x, y, b, and the equation of the least-squares line. (Round your answers for x and y to two decimal places. Round your least-squares estimates to three decimal places.) X= y = b= ŷ= (b) Draw a scatter diagram for the data. Plot the least-squares line on your scatter diagram. y y 22 20 18 16 14 12 10 0 y 22 20 14.4 18 y 22 VX 20 18 16 14 12 10 5 1 (c) Find the sample correlation coefficient r and the coefficient of determination 2. (Round your answers to three decimal places.) 16 14 12 5 2 3 4 19.9 14.4 19.6 20.0 1 1 2 2 3 3 4 4 5 22 6 20 18…