# Thread: Probability (A challenging one)

1. ## Probability (A challenging one)

Suppose a random sample of size n=6 is drawn from the uniform pdf f_Y(y;theta)=(1/theta), 0<=y<=theta for the purpose of using theta (hat) = Y_max to estimate theta. Calculate the probability that theta hat falls within 0.2 of theta given that the parameter's true value is 3.0. A pdf derived in class for theta hat = Y_max is the following: f_Y_max(y) =
(n/theta^n)*y^(n-1).

I'm pretty much completely lost with this one so any help would be great.

2. Originally Posted by eigenvector11
Suppose a random sample of size n=6 is drawn from the uniform pdf f_Y(y;theta)=(1/theta), 0<=y<=theta for the purpose of using theta (hat) = Y_max to estimate theta. Calculate the probability that theta hat falls within 0.2 of theta given that the parameter's true value is 3.0. A pdf derived in class for theta hat = Y_max is the following: f_Y_max(y) =
(n/theta^n)*y^(n-1).

I'm pretty much completely lost with this one so any help would be great.
Calculate $\Pr(2.8 \leq \hat{\theta} \leq 3.2) = \int_{2.8}^{3.2} \frac{n}{\theta^n} \, y^{n-1} \, dy$.