A person has 11. keys and cannot remember which key opens the front door. She chooses each key in turn, so she may be able to open the door on the rst try, second try and so on. Let K be the random variable representing the number of the attempt that actually opens the door. (A) What is the sample space for the random variable K. {B} Calculate the Probability Mass Function PER} and display the result. {C} Calculate the expected value of of the random variable If, ELK]. {D} If instead of choosing each key in turn: shejust randomly selects a new key at each attempt, state the probability mass function for the probability of rst success on attempt k. Calculate the expected value of k in this case