4. A district court judge presides over many court cases each day. Let the random variable X= the number of cases on a randomly selected day in which she declares the defendant guilty. The distribution for the random variable X is given below: # of guilty N A u verdicts Probability 0.05 0.10 0.20 0.25 0.25 0.15 a) What is the expected value of the number of guilty verdicts in a day? b) What is the standard deviation of the number of guilty verdicts in a day? c) If we selected two days at random, what is the probability that the judge declares exactly nine defendants guilty over those two days? d) If we selected two days at random, what is the probability that the judge declares at least nine defendants guilty over those two days