Exercise 1. Exponential Random Variable is Memoryless. The time T until a new light bulb burns out is an exponential random variable with parameter λ. Jane turns the light on, leaves the room, and when she returns, t time units later, finds that the bulb is still on, which corresponds to the event A = {T > t}. Let X be the additional time until the bulb burns out. What is the conditional CDF of X, given the event A?