Assume that the four temperature variables in Table A.1 are MVN-distributed, with the ordering of the variables in x being [MaxIth, MinIth, MaxCan, MinCan] T . The respective means are also given in...

Assume that the four temperature variables in Table A.1 are MVN-distributed, with the ordering of the variables in x being [MaxIth, MinIth, MaxCan, MinCan] T . The respective means are also given in Table A.1, and the covariance matrix [S] is given in the answer to Exercise 10.7a. Assuming the true mean and covariance are the same as the sample values,

a. Specify the conditional distribution of [MaxIth, MinIth]^T, given that [Max_Can, Min_Can]
^T
= [31.77, 20.23]^T
(i.e., the average values for Canandaigua).

b. Consider the linear combinations b₁
= [1, 0, –1, 0], expressing the difference between the maximum temperatures, and b₂
= [1, –1 –1, 1], expressing the difference between the diurnal ranges, as rows of a transformation matrix [B] T . Specify the distribution of the transformed variables [B]
^T
x.