Bitcoin 20 min
You have just made a Bitcoin transaction and you are eager to see if it appears in the next block. You know that the expected time between Bitcoin blocks is 10 minutes. You check the log of your Bitcoin node.
It has been 7 minutes since the previous block. You recall that blocks occurrences in Bitcoin are a Poisson process, which is memoryless. Even though it has been 7 minutes since the previous block, you still expect to wait another 10 minutes.
No new blocks have appeared. It has now been 12 minutes since the previous block. All your waiting has not changed anything. Even though you have bitcoin 20 min waiting for 5 minutes, the math says that you are still expected to wait 10 minutes before the next block will appear.
A Poisson process is memoryless. Because Poisson processes are memoryless, at any given time we always expect that the next block will appear, on average, in 10 minutes. This holds no matter how long we have already been waiting. This memorylessness property applies just as well backwards in time as it does forwards in time. That is, if you pick a random point in time, on average, the previous block will have been mined 10 minutes earlier. This is clear because if you sample a series of events from a Poisson process and take a second sample and reverse the occurrences of that series of events, the two samples will be indistinguishable.
Therefore, by this symmetry, it must be the case that when you pick a random point in time, the expected time until the next event is the same as the expected time since the previous event. You are saying that, if I pick a random point in time, we expect the previous block to have been mined 10 minutes in the past, and we expect that the next block will be mined 10 minutes in the future.
Correct, that is exactly what I am saying. If you pick a random point in time, you expect 20 minutes between the previous block and the next block on average. To compute an expected value we need to know which distribution we are computing the expected value with respect to.
Suppose we observe the Bitcoin blockchain for a while, and bitcoin 20 min make a list of the time between each successive block.
When we average this list of numbers, we will get a value that is close to 10 minutes. Averaging this way corresponds to a distribution where each block interval is sampled with equal probability. Suppose we observe the Bitcoin blockchain for a while, and every day we write down the duration of the block whose interval crosses the 9: When we average this list of numbers, we will get a value that is close to 20 minutes.
Averaging this way corresponds to a distribution where each block interval is sampled, not with equal probability, but proportional to how long the interval lasts. For example, we are twice as likely to sample an interval that lasts for 14 minutes than we are to sample an interval that lasts for 7 minutes simply by virtue of the fact that 14 minute intervals last twice as long as 7 minute intervals.
We can take the pdf for the exponential distribution above and multiply it by a linear factor to reweight the probabilities in accordance with bitcoin 20 min long the interval is. We can double-check this result by recalling the time reversing symmetry argument above. When we pick a random point in time, the time until the next block is some random variable X whose pdf is pdf 1and the time since the previous block is bitcoin 20 min random variable Y whose pdf bitcoin 20 min also pdf 1.
We can compute the distribution for this sum by taking the convolution of pdf 1 with itself, and we indeed get bitcoin 20 min 2 as a result. The bias towards picking longer blocks intervals by using the second sampling method accounts for the discrepancy between the two bitcoin 20 min results when computing average block interval durations. This other sampling method bitcoin 20 min not incorrect or with prejudice; it is simply a different way of sampling.
The distribution of intervals you need bitcoin 20 min use depends on the application you are using it for. If you want to compute the throughput of the Bitcoin 20 min, you will need to use the exponential bitcoin 20 min. Does this sound familiar? This phenomenon is real.
You can't use these points and then at the next breath complain that there's nowhere to spend crypto. Increaseyour Bitcoins now. Vice Media.