Solve the question assuming everywhere a fair coin:

a) Let X be a number of independent tosses that are required for getting heads (H). What is E[X]?

b) Let X be a number of independent tosses that are required for getting 2 consecutive heads. Let the expected number of such tosses be g = E[X]. Notice that if your first toss is tails then you waisted a toss. You now have to do at least 1 + g tosses with probability 1/2. If you get H and then T, you waisted 2 tosses and have to do 2 + g with probability 1/4. Finally, you can get consecutive heads right away with probability 1/4 after 2 tosses. Given that information, construct an equation for g. Solve for g.

c) Generalize part (b.) to the case of N consecutive heads. What is the expected number of tosses of a fair coin to get 2021 consecutive heads?