These are my questions.

a) [2 pts] What is the distribution of yjj, for , i = 1,2,3; j = 1,2, ..., J? b) [10 pts] Show that maximizing the likelihood is equivalent to minimizing the function: 16 Q i=1 =1 c) [10 pts] Find the maximum likelihood estimate (MLE) of Mi, i = 1,2,3. d) [6 pts] The main idea of one-way ANOVA is to partition the sum of squares total (SST) into sum of squares from different sources, namely the sum of squares of the errors (SSE) and the sum of squares of the treatments (SSTr). What distribution does SSTr/ 2 follows? If the distribution involves degrees of freedom, provide the explicit number of degrees of freedom.A study compared the calorie contents of three types of sandwiches: beef, chicken and turkey. We considered / =16 sandwiches of each type. Consider the one-way ANOVA model Vij = Mi + Eij with the Eij's independent and &;; ~N (0,o2), i = 1,2,3; j = 1,2, ...,J.TABLE 3 Percentiles of the x2 Distribution-Values of Xp Corresponding to P P Xp df X:005 X.01 X.025 X.os X.10 X.30 X.95 X.975 X.90 X.095 000039 .00016 00098 0039 0158 2.71 3.84 5.02 6.63 7.88 .0100 0201 0506 1026 .2107 4.61 5.99 7.38 9.21 10.60 AWNE .0717 115 216 352 .584 6.25 7.81 9.3 11.34 12.84 .207 297 .484 .711 1.064 7.78 9.49 11.14 13.28 14.86 .412 .554 831 1.15 1.61 9.24 11.07 12.83 15.09 16.75 676 .872 1.24 1.64 2.20 10.64 12.59 14.45 16.81 18.55 .989 1.24 1.69 2.17 2.83 12.02 14.07 16.01 18.48 20.28 10 00 NO 1.34 1.65 2.18 2.73 3.49 13.36 15.51 17.53 20.09 21.96 1.73 2.09 2.70 3.33 4.17 14.68 16.92 19.02 21.67 23.59 10 2.16 2.56 3.25 3.94 4.87 15.99 18.31 20.48 23.21 25.19 11 2.60 3.05 3.82 4.57 5.58 17.28 19.68 21.92 24.73 26.76 12 3.07 3.57 4.40 5.23 6.30 18.55 21.03 23.34 26.22 28.30 13 3.57 4.11 5.01 5.89 7.04 19.81 22.36 24.74 27.69 29.82 14 4.07 4.66 5.63 6.57 7.79 21.06 23.68 26.12 29.14 31.32 15 4.60 5.23 6.26 7.26 8.55 22.31 25.00 27.49 30.58 32.80 16 5.14 5.81 6.91 7.96 9.31 23.54 26.30 28.85 32.00 34.27 18 6.26 7.01 8.23 9.39 10.86 25.99 28.87 31.53 34.81 37.16 20 7.43 8.26 9.59 10.85 12.44 28.41 31.41 34.17 37.57 40.00 24 9.89 10.86 12.40 13.85 15.66 33.20 36.42 39.36 42.98 45.56 30 13.79 14.95 16.79 18.49 20.60 40.26 43.77 46.98 50.89 53.67 40 20.71 22.16 24.43 26.51 29.05 51.81 55.76 59.34 63.69 66.77 60 35.53 37.48 40.48 43.19 46.46 74.40 79.08 83.30 88.38 91.95 120 83.85 86.92 91.58 95.70 100.62 140.23 |146.57 152.21 158.95 | 163.64Percentiles of the t distribution Values of tr corresponding to P A .. unnnnmnr 1 [.316 6.314 [2.106 31.821 63.651 2 .239 .611 [.1151 1.336 2.920 4.303 6965 9.925 3 .211 .534 .913 1.633 2.353 3.132 4.541 5.341 4 .211 .569 .941 1.533 2.132 2.116 3.141 4.604 5 .261 .559 .920 1.416- 21115 2.511 3.365 4.1132 6 .265 .553 .9116 1.440 1.943 2.441 3.143 3.101 1 .263 .549 .396 1.4\" 1.395 2.365 2993 3.499 3 .262 .546 .339 1.391 1.360 2.306 2.396 3.355 9 .261 .543 .883 1.353 1.233 2.262 2.321 3.250 It] .260 .542 .319 1.312 1.812 2.223 2.164 3.169 11 .260 .540 .316 1.363 1.196 2.201 2.113 3.106 12 .259 .539 .313 1.356 1.132 2.119 2.631 3.055 13 .259 .533 .310 1.350 1.111 2.160 2.650 3.012 14 .253 .531 .3611 1.345 1.161 2.14.5 2.624 2.911 15 .253 .536 .366 1.341 1.153 2.131 2.602 2.941 16 .253 .535 .365 1.331 1.146 2.120 2.533 2.921 11 .251 .534 .363 1.333 1.140 2.110 2.561 2.393 13 .251 .534 .862 1 3311 1.134 2.101 2.552 2.813 19 .251 .533 .861 1 32.8 1.129 2.013 2.539 2.861 20 .251 .533 .3611 1.325 1.125 2.0116 2.523 2.345 21 .251 .532 .359 1.323 1.121 2.030 2.513 2.331 22 .36 .532 .353 1.321 1.111 2.014 2.503 2. 319 23 .256 .532 .358 1.3l9 1.1l4 2.069 2.500 2. 301 24 .256 .53l .351 1.313 1.111 2.064 2.492 2.191 25 .256 .53l .356 1.3-[6 1.106 2.060 2485 2.131 26 .256 .53l .356 1.3-[5 1.106 2. I166 1.419 2.119 21 .256 .53l .855 1.314 1.103 2. I152 2.413 2.111 23 .256 .530 .355 1.313 1.101 2.043 2.461 2.163 29 .256 .531 .354 1.311 1.699 2 .045 2.462 2.156 30 .256 .530 .354 1.3"] 1.691 2.042 2.451 2.150 40 .255 .529 .35] 1.30.] 1.664 2.D2l 2.423 2.1114 60 .254 .521 .343 1.2% 1.611 2.1110 2.390 2.660 120 .254 .526 .345 1.239 1.653 1.930 2.353 2.611 on .253 .524 .342 1.232 1.645 1.960 2.326 2.516 TABLE 5 Percentiles of the F Distribution: F.95 (m1, n2) (Continued) 71 = degrees of freedom for numerator 10 12 15 20 120 DO 161.4 199.5 215.7 224.6 230.2 234.0 236.8 238.9 240.5 241.9 243.9 245.9 248.0 249.1 250.1 251.1 252.2 253.3 254.3 18.51 19.00 19.16 19.25 19.30 19.33 19.35 19.37 19.38 19.40 19.41 19.43 19.45 19.45 19.46 19.47 19.48 19.49 19.50 AWNE 10.13 9.55 9.28 9.12 9.01 8.9 8.89 8.85 8.81 8.79 8.74 8.70 8.66 8.64 8.6 8.59 8.57 8.55 8.53 7.7 6.94 5.59 6.39 6.26 6.16 6.09 6.04 6.010 5.96 5.91 5.86 5.80 5.77 5.75 5.72 5.69 5.60 5.63 6.61 5.79 5.41 5.19 5.05 4.95 4.88 4.82 4.7 4.74 4.68 4.62 4.50 4.53 4.50 4.46 4.43 4.40 4.36 5.99 5.14 4.76 4.53 4.39 4.28 4.21 4.15 4.10 4.06 4.00 3.94 3.87 3.84 3.81 3.77 3.74 3.70 3.67 5.59 4.74 4.35 4.12 3.97 3.87 3.79 3.73 3.68 3.64 3.57 3.51 3.44 3.41 3.38 3.34 3.30 3.27 3.23 5.32 4.46 4.07 3.84 3.69 3.58 3.50 3.44 3.39 3.35 3.28 3.22 3.15 3.12 3.08 3.04 3.01 2.97 2.93 5.12 4.26 3.86 3.63 3.48 3.37 3.29 3.23 3.18 3.14 3.07 3.01 2.94 2.90 2.86 2.83 2.79 2.75 2.71 1.96 1.10 3.71 3.48 3.83 3.22 3.14 3.07 3.02 2.98 2.91 2.85 2.77 2.74 2.70 2.66 2.62 2.58 2.54 4.84 3.9 3.59 3.36 3.20 3.09 3.01 2.95 2.90 2.85 2.79 2.72 2.65 2.61 2.57 2.53 2.49 2.45 2.40 1.75 3.8 3.49 3.26 3.11 3.00 2.91 2.85 2.80 2.75 2.69 2.62 2.54 2.51 2.47 2.43 2.38 2.34 2.30 /12 = degrees of freedom for denominator 4.67 3.81 3.41 3.18 3.03 2.92 2.83 2.77 2.71 2.67 2.60 2.53 2.46 2.42 2.38 2.34 2.30 2.25 2.21 4.60 3.74 3.34 3.11 2.96 2.85 2.76 2.70 2.65 2.60 2.53 2.46 2.39 2.35 2.31 2.27 2.22 2.18 2.13 4.54 3.68 3.29 3.06 2.90 2.79 2.71 2.64 2.59 2.54 2.48 2.40 2.33 2.29 2.25 2.20 2.16 2.11 2.07 1.49 3.6. 3.24 3.01 2.85 2.74 2.66 2.59 2.54 2.49 2.42 2.35 2.28 2.24 2.19 2.15 2.11 2.06 2.01 4.45 3.5 3.20 2.96 2.81 2.70 2.61 2.55 2.49 2.45 2.38 2.31 2.23 2.19 2.15 2.10 2.06 2.01 1.96 1.41 3.55 3.16 2.93 2.77 2.66 2.58 2.51 2.46 2.41 2.34 2.27 2.19 2.15 2.11 2.06 2.02 1.97 1.92 .38 3.52 3.13 2.90 2.74 2.63 2.54 2.48 2.42 2.38 2.31 2.23 2.16 2.11 2.07 2.03 1.98 1.93 1.88 1.35 3.49 3.10 2.87 2.71 2.60 2.51 2.45 2.39 2.35 2.28 2.20 2.12 2.08 2.04 1.99 1.95 1.90 1.84 1.32 3.47 3.07 2.84 2.68 2.57 2.49 2.42 2.37 2.32 2.25 2.18 2.10 2.05 2.01 1.96 1.92 1.87 1.81 .30 3.44 3.05 2.82 2.66 2.55 2.46 2.40 2.34 2.30 2.23 2.15 2.07 2.03 1.98 1.94 1.89 1.84 1.78 1.28 3.42 3.03 2.80 2.64 2.53 2.44 2.37 2.32 2.27 2.20 2.13 2.05 2.01 1.96 1.91 1.86 1.81 1.76 4.26 3.40 3.01 2.78 2.62 2.51 2.42 2.36 2.30 2.25 2.18 2.11 2.03 1.98 1.94 1.89 1.84 1.79 1.73 4.24 3.3 2.99 2.76 2.60 2.49 2.40 2.34 2.28 2.24 2.16 2.09 2.01 1.90 1.92 1.87 1.82 1.77 1.71 4.23 3.37 2.98 2.74 2.59 2.47 2.39 2.32 2.27 2.22 2.15 2.07 1.99 1.95 1.90 1.85 1.80 1.75 1.69 4.21 3.35 2.96 2.73 2.57 2.46 2.37 2.31 2.25 2.20 2.13 2.06 1.97 1.93 1.88 1.84 1.79 1.73 1.67 4.20 3.34 2.95 2.71 2.56 2.45 2.36 2.29 2.24 2.19 2.12 2.04 1.96 1.91 1.87 1.82 1.77 1.71 1.65 4.18 3.3 2.93 2.70 2.55 2.43 2.35 2.28 2.22 2.18 2.10 2.03 1.94 1.90 1.85 1.81 1.75 1.70 1.64 1.17 3.32 2.92 2.69 2.53 2.42 2.33 2.27 2.21 2.16 2.09 2.01 1.93 1.89 1.84 1.79 1.74 1.68 1.62 4.08 3.23 2.84 2.61 2.45 2.34 2.25 2.18 2.12 2.08 2.00 1.92 1.84 1.79 1.74 1.69 1.64 1.58 1.51 4.00 3.15 2.76 2.53 2.37 2.25 2.17 2.10 2.04 1.99 1.92 1.84 1.75 1.70 1.65 1.59 1.53 1.47 1.39 3.92 3.07 2.68 2.45 2.29 2.17 2.09 2.02 1.96 1.91 1.83 1.75 1.66 1.61 1.55 1.50 1.43 1.35 1.25 3.84 3.00 2.60 2.37 2.21 2.10 2.01 1.94 1.88 1.83 1.75 1.67 1.57 1.52 1.46 1.39 1.32 1.22 1.00