Have $ x_{1}$ ... $ x_{10}$ r.v from a distribution with PDF:

$$ f(x;\theta) = e^{ - (x- \theta) },\, \theta \leq x \lt \infty $$

Know that $ \theta_{MLE} = Y = min(X_{i}) $

How do I go about finding the PDF of Y?

Have $ X_{1},X_{2},\cdots,X_{10}$ random sample from a distribution with PDF:

$$ f(x;\theta) = e^{ - (x- \theta) },\, \theta \leq x \lt \infty $$

Know that $ \hat{\theta}_{MLE} = Y = min(X_{i},\;i=1,2,\cdots,10) $

How do I go about finding the PDF of Y?

Have $ x_{1}$ ... $ x_{10}$ r.v from a distribution with PDF:

$$ f(x;\theta) = e^{ - (x- \theta) },\, \theta \leq x \lt \theta $$

Know that $ \theta_{MLE} = Y = min(X_{i}) $

How do I go about finding the PDF of Y?

Have $ x_{1}$ ... $ x_{10}$ r.v from a distribution with PDF:

$$ f(x;\theta) = e^{ - (x- \theta) },\, \theta \leq x \lt \infty $$

Know that $ \theta_{MLE} = Y = min(X_{i}) $

How do I go about finding the PDF of Y?