Calculate the probability of reversal - page 2
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Found something in the scriptures:
Found something in the scriptures:
Yeah.... Either I don't understand it or it doesn't say anything about the essence of the question. I'm not so good at maths to understand the meaning of some statements in depth, I need details, with a formula or at least in words. Do it this way and that way and you'll be happy.
I'll read on and think about it... But obviously the problem is not as simple as it seems.
I'll read, I'll think about it... But obviously the task is not as easy as it seems.
Masterpiece. We take a non-Markovian process, calculate the derivative, and get a Markovian process, but a two-dimensional one.
The coordinate and velocity are two random variables. As I understand it, they are independent.
We can also practice with the derivatives - acceleration and so on...
Guys, where'd you get your diploma so cheap? Or is it that you haven't gotten your diploma yet?
Who is good at maths, please help me solve this problem, I can't figure out how to do it.
1. we have a probability density plot for a normal distribution, in a normal distribution there is no memory and the probability of each next step being directed =50%.
2. Suppose we have a person who takes 10 steps, he can step right or left, each next step is independent of the previous one and the probability of going left or right is 50%. Then we can build a table of probability densities and estimate with what probability he will move away from the starting point in 10 steps. The 6th column shows the probability in %. From the table we get that with probability 0.0977% he will move to the right from the starting point for 10 steps or with probability 4.39% he will move 6 steps for 10 steps.
...
I put the numbers in to make it less quotable.
On 1: in probability distributions, and normal distributions in particular, there is no such thing as the direction of the next step at all. Neither is there a next step itself. What you are referring to with the number 50% is unclear.
On 2: This is a combinatorial problem. Specifically, after step 1, the probability of being at point 0 is zero. Only points +1 and -1 have nonzero probabilities. After 2 steps it will be impossible to get to them already, only points -2 0 +2 are possible. After three, points -3 -1 1 1 3 remain possible. And so on: -4 -2 0 2 4; -5 -3 -1 1 3 5; ... The probabilities, as you can see, depend strongly on the step number. Which is not at all characteristic of the very notion of probability as a limit to the relative frequency of an event with an infinite increase in the number of trials. There is no convergence to the limit, although the size of the oscillation of the relative frequency around zero gradually decreases.
Further, off the point. I think it is clear that the position of a point as a result of its consecutive 1-step shift here and there is determined not only by the composition of these steps (number of combinations) but by their ordering as well. Combinatorial calculations in such cases do not use the number of combinations, but the number of placements (https://www.matburo.ru/tv_komb.php).
Masterpiece. We take a non-Markovian process, calculate the derivative, and get a Markovian, but two-dimensional.
The coordinate and velocity are two random variables. As I understand it, they are independent.
We can also practice with the derivatives - acceleration and so on...
Guys, where'd you get your diploma so cheap? Or is it that you haven't gotten your diploma yet?
Please show by example how to solve this problem. The figures can be taken from the first post from the white histogram.
You might be able to solve it. Just explain your "raw data from the histogram" first.
Tell me what are the numbers on it, how are they obtained, what is their meaning.
For what reason do you call them"probability density". That is, the question of the existence of this very distribution and its differentiability (the density is the first derivative of the probability) has already been solved somewhere. Where?
Explain why there are omissions instead of data for odd points. Do you intend to provide this data later, or are you asking for a general solution, for any data.
You might be able to solve it. Just explain your "raw data from the histogram" first.
Tell me what the numbers on it are, how they were obtained, what their meaning is.
For what reason do you call them"probability density". That is, the question of the existence of this very distribution and its differentiability (the density is the first derivative of the probability) has already been solved somewhere. Where?
Explain why there are omissions instead of data for odd points. Do you intend to provide this data later, or are you asking for a general solution, for any data.
The meaning of the histogram is as follows: we take a sample of 10 steps (1 step may be up or down) and measure the distance by which the process moved from the starting point for these 10 steps. Then we take 10 000 samples of such samples and calculate how many percent have gone for -10 steps from the starting point (downwards), then -8, -6 and so on. These percentages are written on the histogram, and values from -10 to 10 are written at the bottom.