Exercise 5 (5 + 5 pts). You roll a fair die several times and keep track of whether or not the roll is even (E) or odd (0). We'll say that a ipop occurs whenemer the even/oddness of the roll is diiferent than the previous roll. For instance, if you roll the die 5 times and the outcome is EEOEO, then you have seen 3 jpops. 1. Consider n independent ips of the die. What is the expected number of ip-ops? Hint: For each roll, What is the probability that you see a ipop? How can you decompose the number of flipops into the sum of simple random variable? 2. What is the expected number of rolls you need to see is: ipops? Hint: How many rolls are needed before the next ipop? rIi'y modeling it as a known random variable. Try to express the number of rolls you need to get it ipops as the sum of known random variables