ASQ Six Sigma Green Belt – Objectives – Hyperledger Part 6

13. Hyperledger Composer (depricated but still tested as far use case

Poison distribution is also for discrete data and when I say discrete, that means the data is the count data here. So before we talk about poison distribution, let’s talk about the difference and similarities between binomial and poisoned distribution. Let’s talk about similarities first, both of these distributions are for discrete data and when I say discrete that means th counting.

Both these measure the number of successes. So earlier also we said that in case of flipping a coin head was a success. So we were measuring number of successes there. Here also you will see that poison also focuses on number of successes. What is the key difference between poisoned and binomial distribution is that in poison distribution the possibilities of success are infinite. So for example, let’s say when I flipped four coins, the maximum number of heads I could get was four.

So there was a limitation on the possibilities of success. Whereas in case of poison distribution there is no limit to the success numbers. Here at the bottom of the slide I have purpose of both binomial and poison distribution. Let’s look at that. Binomial distribution is one in which the probability of repeated number of trials are studied. We looked at that earlier.

What we do in poison distribution is that the poison distribution gives the count of independent events occur randomly with a given period of time. So here we are looking at the number of events in certain period of time. So let’s move further and probably that will help you in having a good understanding about the poison distribution. Let’s look at what are the properties of poison distribution.

This is something which we did for binomial as well. So in poison the experiment resulted in outcomes that can be classified as success or failure, exactly like what we did in binomial. The second point here is that the average number of successes mu that occurred in a specific region or specific time are known. So here we know the average rate of success, average number of successes. So here we will be taking an example where we will be talking about number of people standing in queue. So there is a bank counter or a teller counter, how many people are in queue waiting for their turn? This is the example which we will be taking in poison distribution.

Here if I look at the second bullet which says that the average number of successes that occur in a specified region or time are known. So what we know here upfront is what is the average number of people standing in queue? So let’s say based on the past history we know that within ten minutes period 3. 6 people come for the bank counter on the average. This is something which we know based on the history.

So we have taken number of measurement, number of times we have counted and we found that on the average ten minutes period 3. 6 people come for the banking purpose and now, what we want to do in posture distribution is based on this mu or based on this average. We want to find out what is the chance that in a ten minute period slot one person comes. In that ten minute slot, five person come, ten people come. That’s something which we’ll be doing as an example in this distribution.

Now, let’s come back to these points which are the properties of poison distribution. The third number is outcomes are random occurrence of one outcome does not influence the chance of other outcome of interest. This is exactly similar to what we did in Binomial. Also, flipping a coin once doesn’t change the chance of head coming in the next flip similar to this number of people coming in ten minutes now doesn’t affect the number of people coming in next ten minutes. And the fourth bullet here is that the outcomes of interest are rare relative to possible outcomes. Let’s think what is the possibility how many people can come in ten minutes? Maybe 1 million people can come in that ten minute and stand in the queue. Who knows? So here the possibilities are infinite.

This is something which clearly makes it different from the Binomial distribution. Some examples of this could be, let’s say a road accident in a city. On the average average, let’s say 1. 3 accidents happen every day. Then based on that you can find out what is the probability that on a given day one accident happens, two accident happens and so on. This is one example. Second example is the Q at the counter which we will be talking about later when we take an example. So these are the properties of poison distribution.

14. Hyperledger Composer Demo

Formula which is p x comma mu is equal to E to the power minus mu to the power x divided by x factorial. Let’s understand each of these items. What does this item mean? Let’s start with p x comma Mu. This is the probability that x number of successes occur when you have the average number of successes as Mu. Let’s talk about the example which we are taking in this example there are 3. 6 people who come on the average in ten minutes period. So Mu is 3. 6 people and then X is for whatever number we want to calculate the probability. So let’s say if we want to find out what is the probability that in these ten minutes five people come, then X will become five coming to the next thing in this which is E to the power minus Mu. E is a constant, the value of which is 2. 718 to eight.

And E is the base of natural logarithmic system each calculator has E value in that. So let’s say if you decided to use this particular calculator for your exam which is ti 30 x a here if you see on the top here. Here is the E to the power x. So if I want to find E to the power minus five, so I can put minus five and then press this button and this one comes after pressing green button because this is at the top. Now, coming to the next item here which is Mu is the mean which we already talked about. And X is the number of successes which we are looking for. So this is the formula for calculating the probability. Now let’s use this formula. And here is one example that on a book encounter.

On the average 3. 6 people come every ten minutes on weekend. So now what I want to do is I want to find out what is the probability of getting seven people in ten minutes. So for that what you do is Mu is equal to 3. 6 because that’s the average which we have already talked. X is equal to seven because at that level or for that number you want to calculate the probability so x is equal to seven. And then probability of PX comma mu is given by this formula and here. If you put those values e to the power -3. 6 and 3. 6 to the power seven divided by seven factorial.

So once you solve this this will give you a value of zero 424. So here in this calculation there are two important things which if you are not clear about, let me explain those and these are how to find the value of E to the power -3. 6 and how to find out the value of factorial seven. So here is the calculator so let me come a little bit near to this. And here I can show you. So this is the calculator. So if you want to find out factorial seven so what you need to do is first thing is switch on the calculator. So I switch it on now, this is on. Now, what I need to do is press seven. Because I want to find out factorial seven.

So I press seven. So here I have seven and then factorial is somewhere here above three and and in the green color. So for that, what I need to do is press this second and press this number three. This will give me factorial. Seven, which comes out to be 540. So this is how you find out the factorial value. And how do you find out e to the power -3. 6 so for that let me clear this so I clear this. And now what I want to find out e to the power -3. 6. So for that I need to first press 3. 6 and minus sign. So I’ll press 3. 6. And with the minus sign is here. So now I have -3.

6 now I need to put E to the power X and which is here above Ln. So for this I press second and I press this button this gives me e to the power -3. 6 which comes out to be 0. 02,732, which is what you see on the slide. So this is how you calculate these values. And you come out with this number which is 0. 424, which means there is a 4. 24% chance that you can have seven people coming in those ten minutes. So this was the way to calculate the probability using calculator and using the formula. If you are using Excel sheet in Excel there is a built in function which is poison disk. You can use that. The next thing which you want to put in the bracket is the value of X which in our case is seven, then comma 3. 6, which is the mean. And then comma false. And why you say false? Because here you are not looking at the cumulative one cumulative would be the chance of getting seven people or less.

So that probability will include the probability of getting seven people, probability of getting 654320. And addition of that will come if you put two instead of false here. But since we just wanted the probability of seven people, we put false and we got the same value which we got using the manual calculation. So earlier we took this example to find out the probability of getting seven people in the queue in ten minutes. What I did was using minitab I plotted this particular distribution which gives me the probability of each of these type of events what’s the probability of getting zero person in ten minutes. There is some chance of that which is roughly let’s say around maybe two to 3% chance that no one comes to the counter in ten minutes. Then you have around 10% chance that one person comes. And then there is around let’s say 17% chance that two people come to the counter in ten minutes period and so on.

So this gives me the complete poison distribution for this type of event where the mean is 3. 6 and it gives me the probability of each type of occurrence, the chance of getting 0%, one person and so on. And this particular graph goes on till infinite. There is a chance that you might get 500 people in ten minutes even though the probability of that is very very low. So the tail on the right will be very long which will go till infinity but tail on the left will stop at zero because you will not get less than zero people in ten minutes. So this is your poison distribution. Now coming to few more important properties of poison distribution and as we talked in binomial in binomial also we talked about the mean and the variance of the distribution. We calculated that using formula like MP which was for mean and so on, in poison the mean of the distribution is equal to mu.

So in this particular example the mean is 3. 6. So on the average on the long run you will get 3. 6 people coming to the queue in ten minutes period. This is mu. A very special property of poison distribution is that in poison distribution the variance is also equal to mu. And as far as the exam is concerned there is a good chance that in some way or other way you might get a question where you are asked that in which type of distribution you have the mean and variance as equal. So this is the poison distribution where you have have the variance which is equal to mean and here I’m saying variance. So remember that this is the variance which is equal to the mean. The standard division is the square root of the variance, hence the standard division will be square root of mu.