Question

mention the uses of wilk's lambda in testing a mean vector of a multivariate normal population.

Answer 1

Wilks' lambda is a test statistic used to test whether there are differences between the means of identified groups of subjects on a combination of dependent variables.
Wilks' lambda performs, in the multivariate setting, with a combination of dependent variables, the same role as the F-test performs in one-way analysis of variance. Wilks' lambda is a direct measure of the proportion of variance in the combination of dependent variables that is unaccounted for by the independent variable (the grouping variable or factor). If a large proportion of the variance is accounted for by the independent variable then it suggests that there is an effect from the grouping variable and that the groups have different mean value.