Problem 1

Let \(X_1,...,X_{100}\sim Exp(1.3)\), independent, and let \(S=\sum _{i=1}^{100} X_i\). Find \(P(S>100)\)

  1. directly
  2. using the CLT

Problem 2

Let \(X_n\sim U[0,1]\), n=1,2,.., and independent. Use the CLT to find \(P(\sum_{i=1}^{50} X_{i}>24)\). Give an upper and a lower bound for this probability.