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).