2. We say the rv X has the "W" distribution with parameter q > 0 (written...

2. We say the rv X has the "W" distribution with parameter q > 0 (written X ~ W(q) ) if X has pdf f(x)= 2x/q^2, for 0 < x < q, and f(x) = 0, elsewhere. Consider the parameterized "W" family {W(q) : q > 0 }. a) Let Yn be the maximum of the random sample of size n from W(q). Show that Yn is a consistent estimator of q. Note here that is the q is the “population maximum.”) b) Find the probability density function of Yn. (Hint: Find the cumulative distributive function first.) c) Show that Yn is NOT an unbiased estimator of q (Hint: use (b).) d) Show how to “correct” Yn here to make it unbiased, and call your new estimator Tn . Show your new estimator is also consistent, hence unbiased and consistent.

Expert Solution

Consistency here is looked at as in probability convergen,, and thus we proceed.

orchestra answered 2 years ago

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