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Corrected OBVIOUS typo

Finding the PDF of Y, where Y = min X

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?