Please show me step by step solution. Problem 1 Consider an experiment with two factors A (5 levels), B (4 levels). Suppose all possible com- binations of the factors were run with 2 replicates. Write down the complete break-up of the total available degrees of freedom in the ANOVA. Problem 2 Here is a Latin square of order 3. A B C BCA CAB (a) Find another Latin square of order 3 which has the same first row as above. Prove that it is unique (that is, there is only one such Latin Square) and orthogonal to the above Latin square. (b) Hence find a Graeco-Latin Square of order 3. (c) Consider the following Latin Square design of order 4. Design Data Column Column Row 1 2 3 4 Row 1 2 3 4 1 C D B A 1 235 236 218 268 2 A B D C 2 251 241 227 229 3 D C A B 3 234 273 274 226 4 B A C D 4 195 270 230 225 Model: Yijk = +i + j + Tk + ijk, i = 1, . . ., 4; j = 1, . . ., 4; k = 1, . . ., 4, = Average effect, Xi = ith row effect, ;=jth column effect, Tk = kth treatment (i.e., Latin letter; 1 corresponds to A, etc.) effect, Eijk are independent N(0,). Calculate the unbiased estimates of 2, 31 and 73. Also compute SS(Row). (d) What will be the residual degrees of freedom for (c)?