In the notation of Problem 1, prove that the pedigree statistic (Y i Ai) t 1

In the notation of Problem 1, prove that the pedigree statistic

(Y i − Aiµ)

t

Ω−1 i (Y i − Aiµ)

has a χ2 mi distribution when evaluated at the true values of µ and σ2

[30]. This χ2 mi distribution holds approximately when the maximum likelihood estimates ˆµ and ˆσ2 are substituted for their true values.

There is a slight dependence among the statistics

(Y i − Aiµˆ)

t

Ωˆ −1 i (Y i − Aiµˆ)

because of the functional relationship featured in Problem