How to set up a bitcoin miner? Miners are any computer that is running the Bitcoin software and can leave and reenter at any time. In order to incentivize them to stay on the network and expand CPU power and electricity, they can earn Bitcoin rewards for successfully mining a block and transaction fees. Nowadays, miners use specialized computer hardware called Application-specific integrated circuits (ASIC) that are extremely good at computing hashes in parallel.
A mine can be viewed as a contingent claim, or a call option, on the commodity being mined. Using a framework developed by Morck et al, 1989,  the value of a Bitcoin Mine is characterized by the price of Bitcoin and the inventory of Bitcoin, which we assume are both random variables.
The price of Bitcoin we assume follows a generalized random walk. Or Brownian Motion with drift, which is standard in quantitative finance literature. The inventory of Bitcoin we assume follows a Poisson process.
Moreover, in probability, statistics and related fields, a Poisson point process is a type of random mathematical object. Furthermore, one that consists of points randomly located on a mathematical space. The Poisson point process or simply the Poisson process. But it is also called a Poisson random measure. Poisson random point field or Poisson point field.
This point process has convenient mathematical properties, which has led to it being frequently defined in Euclidean space. And used as a mathematical model for seemingly random processes in numerous disciplines. Such as astronomy, biology, ecology, geology, seismology, physics, economics, image processing, and telecommunications.
Moreover, in order for the miner to have incentive to use his computing power, the miner must receive a reward. If the miner is the first one to correctly compute the correct number that when hashed with say SHA-256. Then the miner will receive a reward with the block reward. This value is halved every 210,000 blocks. Currently, the reward is 6.25 BTC and will drop to 3.125 BTC likely at some point in 2024.
So, find a suitable model for predicting the number of blocks that a miner will mine in some specified time frame. Let us consider a miner with a percentage 0 ≤ p ≤ 1 of the entire Bitcoin network’s hash capacity. This means that the probability of successfully mining a block. In addition, the amount of successfully mined blocks that miner has is proportional to his p of the hash power. On average, the entire network takes about tN0 = 10 minutes to mine the current head of the chain.
As a result, this means that it should take about tM 0 = tN0 /p minutes on average for the miner to mine the block on average. If we now consider the times between successive blocks mined, a random variable T. Because of the nature of the mining process. Specifically the fact that each successive block’s hash is independent of the blocks behind it, we can characterize the mining process as a Markov Process.
Now that we have discussed the overview, for more specific instructions, see CoinDesk’s recent article: Click Here For Article