In: Statistics and Probability
2. Let X be a normal random variance with media 1 and variance 4. Consider a new variance A random variable T defined below: T = -1 if X < -2 T = 0 if - 2 ≤ X ≤ 0 T = 1 if x>0 Find the moment generating function of T and, from it, calculate E (T) and Var (T).