How much time does it take to mine a bitcoin block
This holds no matter how long we have already been waiting. The distribution of intervals you need to use depends on the application you are using it for. Correct, that is exactly what I am saying. We can compute the distribution for this sum by taking the convolution of pdf 1 with itself, and we indeed get pdf 2 as a result. If you want to compute the throughput of the Bitcoin, you will need to use the exponential distribution.
Suppose we observe the Bitcoin blockchain for a while, and we make a list of the time between each successive block. It has been 7 minutes since the previous block. If you want to compute the throughput of the Bitcoin, you will need to use the exponential distribution. The bias towards picking longer blocks intervals by using the second sampling method accounts for the discrepancy between the two different results when computing average block interval durations.
If you pick a random point in time, you expect 20 minutes between the previous block and the next block on average. You recall that blocks occurrences in Bitcoin are a Poisson process, which is memoryless. A Poisson process is memoryless.
The distribution of intervals you need to use depends on the application you are using it for. When we average this list of numbers, we will get a value that is close to 20 minutes. That is, if you pick a random point in time, on average, the previous block will have been mined 10 minutes earlier. We can compute the distribution for this sum by taking the convolution of pdf 1 with itself, and we indeed get pdf 2 as a result.
Even though you have been waiting for 5 minutes, the math says that you are still expected to wait 10 minutes before the next block will appear. It has now been 12 minutes since the previous block. The bias towards picking longer blocks intervals by using the second sampling method accounts for the discrepancy between the two different results when computing average block interval durations. You check the log of your Bitcoin node. This phenomenon is real.
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. You check the log of your Bitcoin node. A Poisson process is memoryless. If you pick a random point in time, you expect 20 minutes between the previous block and the next block on average.