1. When you turn on your computer, a certain bit (0/1) in its memory is initialized to the value 0.
2. (a)Suppose that starting from when you turn on your computer the bit is incremented (adding 1 mod 2) at random instants of time, on average times per millisecond. What is the probability that after t milliseconds the bit stores the value 0?
3. (b)Suppose that starting from when you turn on your computer the bit is rewritten at random in- stants of time, on average times per millisecond, and each rewrite results in a 1 independently with some probability p (and of course a 0 is written with probability 1 p). What is the prob- ability that after t milliseconds the bit stores the value 0? Hint: condition on whether or not a rewrite occurred before t milliseconds.
4. (c)Which probability is larger, assuming the probability p in part (b) is p = 0.5?