Two parts to this question

1/ There have recently been concerns over drops in hash rate observed on sites such as blockchain.com.

However, my understanding is that hash rate is inferred from the difficulty level and the block intervals.

I am trying to work out the exact formula for the inference of hash rate.

I know that the average time we can expect to find a block in is calculated with the following formula:

average time to find a block = (difficulty * 32 ** 2)/ hash rate

Would that mean that hash rate is inferred with the following formula?

hash rate = (difficulty * 32 ** 2)/ time interval between the last two blocks

2/ I mainly want the first part answered but if you are feeling rosy today, an answer to this second part would be amazing.

Block times are Poisson distributed. I understand that this allows us to calculate the probability that block times increase to such an extent over the course of a day that it infers a 40% reduction in hash rate.

Does anyone know the exact calculation which would let us calculate this probability?

Here’s some rough ideas I have about the calculation:

The following formula allows us to calculate the probability that *k* events take place in time period *t*.

P(k in t) = (e ** -lam)*(lam**k / k!)

where lam = (average events which can be expected to be observed per unit of time * t)

The average events which can be expected to be observed in the case of block intervals is 1 block per ten minutes so 1/10

Let’s say we have hash rate dropping 50% over the course of one day, would that imply that we are observing 288 blocks over the course of 1440 minutes?

If I am thinking about this in the correct way, this would mean the calculation is as follows:

P(288 blocks in 1440 minutes) = (e ** -(144)*((144**288)/288!)

Not sure if this calculation is correct. But to take it further, this would calculate the small probability of exactly 288 blocks being found in 1440 minutes. But if it were possible to calculate the Poisson distribution of block intervals, we may be able to find the probability of finding greater than or equal to 288 blocks in 1440 minutes.

As you can probably tell, my understanding of the second part of the question is limited so if you have an answer to even just the fist part, that would be amazing!