Answer Happy

(b) Assume that a block was mined three mimutes ago, and let U be the time in seconds until the next block is mined somewhere in the world. Again carefully explaining your reasoning, name the distribution of the random variable U, give the values of its parameter(s) and specify its mean and variance, (e) What property of the random variable T explains the observation that you made in (b)? (d) Let J be the number of blocks that are mined in an hour worldwide. Name the distribution of the random variable R. give the values of its parameter(s) and specify its mean and variance.
(e) Let S be the length of time, in seconds, that the vendor in (h) above has to wait before six blocks are mined worldwide. Name the distribution of the random variable S, give the values of its parameter(s) and specify its mean and variance. (1) Most Bitcoin miners work for mining pools. Assume that a particular pool, Bitcoin Mining Inc., controls a proportion p of the world's total computing power devoted to Bitcoin mining and let JA be the number of blocks mined by Bitcoin Mining Inc in an hour. Conditional on the random variable J in (d) being equal to j, what is the distribution of JA? Use the Theorem of Total Probability to derive the distribution of JA and hence its mean and variance.