well, without doing any math I'm sure Y1 is BIASED for theta
unbiased is
But since the density of Y1 will be between theta and 1 there is no way it's expected value can be either endpoint.
Let Y1<Y2<Y3 be the order statistics of a random sample from a Uniform distribution.
1) Show that Y1 is an unbiased estimator of
2)Find an unbiased estimator of and that it is unbiased.
Thanks for the help, biased and unbiased have always confused me
attempt of an answer to show that Y1 is a biased estimator of
Y1 being the minimum of the order statistic, i get that the distribution of the minimum is
after plugging in
and then to get the expected value of Y1 i get the from to 1 of Y1 times f(y1)
am i in the right direction or completely off?
Hi,
I have gone through the steps on a similar type of problem - the main difference is that the distribution is with n > 10 and .
I found the MLE's to be
and
I'm trying to show whether they are biased on unbiased. I get the density and it looks like Beta (1, n) and Beta (n,1) for and , respectively, except that I have an extra term of
in the function.
I am not sure what to do with that - do I just multiply the mean of the beta function with that fraction? It seems like I would need to "do something" with it in order for the equation to integrate to 1?
I would love a hint... Thanks!
This is not a Beta distribution... Especially with the support ! With a substitution, you can get something like n(1-t)^(n-1) (the 1/(theta2-theta1) simplifies with the du).
But it's not a Beta distribution.
Your pdf is correct though you have to state the support, in which interval it belongs. Namely
In order to find its expectation, just calculate , like you would do for any other random variable.