1. Let {X_i: iN} be defined as in the previous problem. Let X_[1]denote the random variable defined as

X_[1]= min{X₁,X₂,...,X_n}

Similarly, let X_[2] be defined as

X_[2]= min{X_i: i N\[1]}

1. Are X_[1]and X_[2]independent ? Explain.
2. Give an expression for the distribution and density functions of X_[k]. Hint: let I_ibe the indicator random variable of the event{X_i x}. It follows that {^XI_i k} = {X_[k] x} iN