Estimation of an exponential parameter


I´m having a hard time trying to figure out this.

Let X1,..,Xn be i.i.d. Exp(λ) random variables, where λ is unknown.
What is the distribution of min(Xi)? Enter the pdf f_min(x) of min(Xi) in terms of x .

My approach
Since the pdf of an exponential is λ *e^(−λx) and the first term X1=0 regarding the pdf of the distribution.
the pdf would be λ *e^(−λ(0))=λ *1=λ 
this is my hint: You can proceed with the definition of Survival Function as below


Now you can easily get the CDF(z) and the corresponding pdf(z) by simply deriving the CDF with respect to z
Generally speaking, the question has a common answer: the CDF of the min of n iid random variables is given by the following formula

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