ASQ Six Sigma Green Belt – Objectives – Hyperledger Part 2

4. Whiteboard – Hyperledger Fabric Channels

Two main things which we are doing here include the basic probability concepts and the second thing is central limit theorem. Let’s start with basic probability concepts. Here in basic probability concepts we will be talking about different types of events, independent events, mutually exclusive events, multiple rules, permutation and combinations. And even before these we will be talking about some basic concepts related to probability.

Understand the definition of that? Understand? How do we calculate probability? Let’s start with the basic definition of probability. There are two definitions of probability. One is the classic model and the second is relative frequency of occurrence. Let’s talk of classic model. When we say probability, the probability is equal to the number of outcomes in which the event occurs divided by total number of possible outcomes of an experiment.

Let’s take a very simple example, and that is the example I guess you would have seen in any other place where you start talking about probability. And this is rolling a dice. So on the right side you see a picture of a dice which has six sides, and each of these side has a different number from one to six. So the top of this dice might have number 12345 or six. So if I roll a dice, what is the chance or what is the probability that I will get number two at the top? So there are six possibilities, six are the total possibilities and this is what is the denominator. So denominator is six, because there are six number of total possibilities.

And what I’m looking at is at one single possibility of having two. So one divided by six is equal to one by six is the probability of getting number two at the top when I roll a dice. Another definition of probability is the relative frequency of occurrence. Let’s take another example of me going from my home to office. My normal time is 630. So at 630 I need to be in the office. But you really cannot be at 630. Exactly. Every day there is always a variation in whatever you do.

So what I did was I started recording my reaching time in the office. Sometimes I will reach at 615, sometimes I will reach at 625, sometimes I will reach at 645. What I wanted was to reach at 630. And what I noted down that out of 200 readings which I took, 50 times I was before 630, and 150 times I was at 630 or after 630. Now let’s say today I’m going to office and I’m looking at what is the probability that I reach office before 630 that I can do based on this past history, my past history tells that 50 times I was before 630, and 150 times I was at 630 or after 630. So out of 200 days, only 50 days I was before 630. So what is the probability that today I will be reaching before 630? I can calculate that by 50 divided by 250 is the number of times this event has occurred.

This event means reaching before 630 and the total number of opportunities for an event to occur was 200, which gives me one divided by four. Or there is a 00:25 as the probability that I reach before 630. So this is the definition of probability. With this. Let’s learn about some basic definitions which include experiment or trial. So experiment or trial in previous two examples was rolling the dice was one experiment or me going to office was another experiment or the trial something? Which is done with an expectation of result.

Thus, experiment or trial outcome is the result of that experiment and which in previous case was getting number two or reaching before 630. Another important definition which you need to learn. About. Probability is the sample space. Sample space is all the possible results of that random experiment. So here we are, listing down all, whatever is possible. So let’s take a simple example of dice. What all is possible when? I roll the dice so I can get number 12345 or six. So this is the sample space. If I roll two dices, then this is the sample space. In this sample space, if you see that the first die. Might roll as 1 second, as one, one and two, one and three and so on. So there are 36 possibilities when I roll two dice. ISIS.

5. Demo – Channels

We have a rectangle which shows the sample space or everything, whatever is possible. And this is the rectangle here, this is our sample space. And as we earlier said that when I roll a dice in the sample space I have 123456. So all these possibilities you have in the sample space. Now within the rectangle you can have different circles which show a specific event. Let’s say in this case, the event of my interest is getting number one or number four in roll of dice. And this I say as event number A. So I have event A which is getting one or four in the roll of dice. So that’s what I have shown in the circle, in the circle A I have one and four. So these are event A and anything other than event A is in the sample space because sample space occupies everything, all the possibilities.

So the remaining possibilities which are 2356 are shown outside this circle. So this is how I will show a simple vent diagram. Let’s make it a little bit more complex here. Let’s say I have another event which is event number B, and event B is getting two, three, five or six. So here I have event B which has 2356 in that. And now there’s nothing which is left outside event A or event B. So now if you look at event A and event B, one thing you would see that if event A happens, B cannot happen. If event B happens, A cannot happen. Let’s say when you roll a dice you get one or four, that’s event A, you get two, three, five or six, that’s event B. There is no possibility that both of these events can happen together. If that is the case, then we call those two events as mutually exclusive events. So this is one of the important definition which you need to understand. Mutually exclusive events are those events when two events cannot occur at the same time. Now let’s look at two events which are not mutually exclusive. Here is an example of that. The example of not mutually exclusive event is here, which is event A and event C. Now my event C is different. My event C is getting 1235 or six in roll of dice. Event A is getting one or four. So if I get one in the roll of dice at that time, both event A and event C have happened together.

Event A has happened, C has happened. If the rule of dice gives me number one and that is the reason you see these two circles overlapping and you have number one in the middle or the overlapping area. So if I ask you whether event A or C are mutually exclusive events, the answer to that is no, these are not mutually exclusive events. And why I was showing mutually exclusive events because I want to introduce two important concepts which are union and intersection. Once you have complex probability then you need these two concepts. Let’s say instead of finding out what is the probability of getting number two. Okay, you can very easily say that one by six and what is the probability of getting number two or three or what is the probability of getting number two and three.

When you roll two dices that’s where you need these concepts which are union or intersection. When we talk of union, union is total of everything. So here if I have these two circles when I talk of union, union means or either A or B. And this is shown by symbol U. In case of these two circles, circle A and C how I will show union is union is shown by this whole area. This whole area shows either event A has happened or event C has happened. Whereas when I talk of intersection in these two events the intersection is basically and what does that mean is event A and event B has happened and which is this area, which is the common area and which is this area. So intersection basically represents and that both of these events have happened. Event A and event B has happened. And this is shown by the reverse or the inverted.

6. Whiteboard Hyperledger Fabric Development

We are looking at three different types of events. One is mutually exclusive events and we have talked about that. So let’s say this is our Vend diagram, this is the total sample space and we have event A and event B. Event A and B were mutually exclusive events. Because there is no overlapping area, there is no way both of these events can happen together. So if two events cannot happen together, they are called as mutually exclusive events. And we looked at an example of this earlier. Now coming to the second definition, which is independent events. Here we are looking at that the occurrence of event A doesn’t change the probability of event B. Let’s say if we are rolling a dice. So first time I roll the dice, each of the number from one to six had equal chance of getting either 12345 or six. Let’s say I got number two in the first roll of dice. When I roll the dice second time, will it matter what we got in the first attempt? Whether we got in the first attempt, two or four or six, whatever we got in the first roll of the dice, that is not going to affect the second roll of the dice.

So in this case, these are independent events. So rolling a dice two times are independent events. Same thing is flipping a coin. So if I flip a coin, first time head comes, that doesn’t affect the second time. What will come in second attempt, both head and tail will have the probability of getting zero five. So this was independent event. But then what is dependent event for dependent event? Let’s take an example where in the tray we have certain number of balls. Let’s say we have two red balls and two blue balls. So one red, second red, let’s put it red and there are two blue balls. If I pick one item from this, what is the probability of getting a red ball? The probability of getting a red ball will be two divided by four because there are two red balls and there are four balls in total. So this is the first attempt. Now, let’s say if I got red in the first attempt and I am not replacing that red ball back into the bowl. So now what I am left in the bowel is one red ball and two blue balls. Now, if I ask you what is the probability of getting red ball now? Now the probability of getting red ball will be one by three, not two by four.

Because these two events, event A and event B, when we are picking a ball from the bowl without replacement, then these are dependent events. So that’s something which you need to understand, whether the events are dependent or events are independent. Coming to this third definition, which is complementary event, the complementary event for event A is shown as a dash. So let’s say if PA is the probability of Event A, then the probability of complementary event of A is shown as PA dash. And what is complementary? Complementary is anything other than A.

So let’s say if the event A is getting number two in the role of dice, that’s event A. So let’s say A is equal to getting number two, then A dash will be anything other than A. So that means this will be 1345 or six in a row of dice in case of Venn diagram. So when we draw a Venn diagram in that if this is Event A, then anything outside this event A is a dash. This is your a dash. If you know the probability of A, then you can get the probability of complementary event as one minus the probability of A. In this case when we were talking of getting two in the roll of dice, the probability of A was one by six. Then probability of A dash, which is the complementary event of A will be one minus one by six is equal to five by six.