You roll a fair die several times and keep track of whether or not the roll is even (E) or odd (O). We'll say that a flipflop occurs whenever the even/oddness of the roll is different than the previous roll. For instance, if you roll the die 5 times and the outcome is EEO EO, then you have seen 3 flipflops. 1. Consider n independent flips of the die. What is the expected number of flipflops? Hint: For cach roll, what is the probability that you see a flipflop? How can you decompose the number of flipflops into the sum of simple random variable.? 2. What is the expected number of rolls you nced to see k flipflops? Hint: How many rolls are needed before the next flipflop? Try modeling it as a known random variable. Try to express the number of rolls you need to get k flipflops as the sum of known random variables.

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Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.