3) As on previous let X_1….X_n be i.i.dwith pdf

Question

f_θ(x)= θx^(θ-1)1(0≤θx≤1) where θ>0
a)
Assume we do not actually get to observe X_1…X_n Instead let Y_1… Y_n be our observations where Our goal is to estimate θ based on this new data.
What distribution does Y_i follow?
First, choose the type of the distribution:
Bernoulli
Poisson
Normal
Exponential
Second, enter the parameter of this distribution in terms of θ. Denote this parameter by . (If the distribution is normal, enter only 1 parameter, the mean).
m θ= ?
b)
Write down a statistical model associated to this experiment is the parameter θ identificable
Y
N

Answer 1

Bernoulli
a.
1/(2^theta)

b.
Y

c.
(ln(2))^2/(2^theta-1)

d.
-ln(barY_n)/ln(2)

e.
-ln(barY_n)/ln(2)

f.
(2^theta-1)/(ln(2))^2

g.
1-Phi(sqrt(n/V)*(hattheta-1))
no