Question: 4.2. Suppose a random sample of size n = 6 is drawn from the uniform pdf \({{f}_{Y}}\left( y;\theta \right)=\frac{1}{\theta }\), \(0\le y\le \theta \), for the purpose of using \(\hat{\theta }={{Y}_{\max }}\) to estimate \(\theta \).

(a) Calculate the probability that 6 falls within 0.2 of 0 given that the parameter's true value is 3.0.

(b) Calculate the probability of the event asked for in Part (a) assuming the sample size is 3 instead of 6.