(Or foo = FEXTH for PEX= 2. , good ~ Unit for = = 70. so . for is always thereas maxx fix) = 2. ( 2+ 1) = 5 90 ~ Urif(1 2 ) there fore Want M 1 M Z FOX aut (b ) maxx for ) = s when azz go) ~ unit 10, 10 ) = - IT - 0 Mg ( 2 ) 2 fly M M Z 2. Let f (2:) and 9(a) be the target and trial distributions, respectively, in the rejection sampling method. Find the Optimal constant M that maximizes the acceptance rates for the following designs. (a) f(:1:) = (:1:+ 1) fer 1 S x E 2; 9(33) ~ Unif(l, 2). (b) f(:L') = sinx for 0 S :5 5 7r; 9(3) ~ Unjf(0,7r). . Implement the rejection sampling design in 1(b). Generate 500 samples from the trial distribution Unif(0, 7r). (a) What is the acceptance rate of the 500 samples you generated? (b) Plot the histogram of the accepted samples