- #1

stukbv

- 118

- 0

## Homework Statement

(x1,x2,...xn) is modeled as observed values of independent random variables X1,X2,...Xn each with the distribution 1/θ for x in [0,θ] and 0 otherwise.

A proposed estimate of θ is m = max(x1,...xn) Calculate the distribution of the random variable M=max(X1,X2,...Xn) and considering M as an estimator for θ, its bias and mean squared error.

**2. The attempt at a solution**

P(max(X1,...Xn)≤m) = P(X1≤m)P(X2≤m)...P(Xn≤m)

via independent of the Xi's.

Then since they have the same distribution this is just

(m/θ)

^{n}

So to get the distribution do I just differentiate with respect to θ

Which would give me

n(m/θ)

^{n-1}* (-m/(θ

^{2}))

Is this the right way to think about it ?

Thank you

Last edited: