Let Xi be iid Exp(λ) random variables.1. Let Mn = max1≤i≤n Xi. Compute the CDF FMn (x).2. Using the identity P(X > x) = exp(−λx), show that if an = log n, and Yn = Mn − an, thenFYn(x) → e^(-e^-x).3. * What does this say, heuristically, about the order of magnitude of Yn?

Let Xi be iid Exp(λ) random variables.
1. Let Mn = max1≤i≤n Xi
. Compute the CDF FMn (x).
2. Using the identity P(X > x) = exp(−λx), show that if an = log n, and Yn = Mn − an, then
FYn(x) → e^(-e^-x)
.
3. * What does this say, heuristically, about the order of magnitude of Yn?