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

**Exercise**

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*