That's the last popcorn. Nope, there's still popcorting. The rest of the popcorn's getting burnt. That's what happens during the time of those.  These guys are the fresh popcorns. And then there's probably a lot of kernels somewhere that forgot that they were going to attend the talk. OK, do I have to, like, say something to start? Or, like, do I just start? It's your poor bit. OK, I don't have a clicker, right? OK. So hello, everyone. I am Karine Wallach. I lead the developer community at a company called StarTree. We build developer tools. It's kind of managed solutions around Apache Pino. If you're curious, you can look it up. It's pretty cool stuff. But today I'm here to talk to you about community stuff. So the topic, which you guys already know because you're here, is turning users into advocates and doing it at scale. So just starting off, just a little bit of background about me. I'm not going to dig too much into this. But basically, I kind of fell into doing community. I started organizing happy hours for me and my girlfriends because I realized that when we talk to each other, things happen. And then I ended up starting a women's networking group. I launched it in New York City. And I also launched one in Philadelphia. And I was running it for, it was free for everyone to come in and whatever was pretty cool. And all contributed from the community. And I was running that for 10 years. Still kind of exists, but it kind of fizzled out a little bit. And then after that, I used to work in rap music before I got into technology. I literally was doing marketing for M&M and 50 Cent. And then I found my way into tech. And when I did, my first official community role was my last job. I was working at Neo4j. It's a graph database company. Really, really, really freaking cool. Highly recommend to take a look at it if you are, if you like networks and connections and stuff, it's really, really cool. And it's a very relevant community. And then since then, about two years ago, I joined StarTree, which is a company I currently work at now. We're an early stage startup. Yeah, pretty early. I don't know, we're 70 people. So I guess it's not that early. And working on building the community around StarTree and Pino, we have the open source Apache Pino project that we are a very big supporter of. So I'm gonna kind of work a little bit backwards as I'm kind of presenting this story to you. And I'm gonna tell you stories and then just kind of give you the lessons that I've learned from it. But hopefully there'll be like some actual tactical takeaways that you can take from this presentation. Okay. So first, when I got to Neo4j, this was like my first time doing kind of like an official community development role. And there were some observations that I had. So one, the community there was really healthy. There was like a lot of really engaged people. And I was trying to understand like what caused it to be this like healthy engaged community. And I blame it on this guy. Michael Hunger, he was basically, he's been with Neo4j for like, I don't know, since it was born 10 years ago or something like that. But one thing that he was consistently doing, I mean, he was doing all kinds of developer advocacy work, answering questions, things like that. But he was always recognizing people for the small contributions that they made. And he was calling it out and thanking them. So it was just consistent. Wow, thank you so much. That was so great. Did you see how this person did this thing? Just consistent, privately and publicly. And I think that that is one of the largest reasons on why this community was so healthy. Like, nobody was ignored. People were noticed for all the things that they did. And that is huge. So, the three big things, this is, sorry. I'm like looking at my speaker notes. I could see it right in front of me. And I still choose to like, let me just wait. Okay, so the three big things, the gratitude, the recognition and inclusion. So he was always bringing people in. So like, whenever they were working on anything, he'd always say, well, we have to ask this person, include this person, include that person. Bringing everybody in to the conversation. And those are the things that I think were like really the big cause of like, what made this community so healthy to start off with. I got really lucky jumping into the healthy community. Very good experience. So, I'm gonna kind of just kind of go over like the community ecosystem. This is overall on how I look at community. First of all, when you're asking for any kind of contributions from your users, any kind of advocacy work or writing or whatever it might be, whenever you're thinking about what kind of contributions you want them to make, you wanna make sure that it's going to matter to the rest of the community. And that is really important. You have to create contribution requests that actually circle back. Now, the benefit of that and the reason why it's so important to do this is because you want to ultimately create some kind of feedback loop, right? Where like the rest of your community is grateful and recognizing the people for the contributions that they're making. So, let's see. This is the ecosystem that I found online, which I thought was kind of interesting, but so if you're doing something that's like community development where like your goal is like product feedback, for example, right? You wanna make sure that somebody on the product team actually cares about what these people are providing, right? So like this feedback loop, it's really, really important. So like if you're asking for like contributions that are blog posts, you wanna make sure that people are actually reading them or the content is actually relevant to the community. So I think this is like a really important point to note. Okay, so in the ecosystem, just going back to this picture really quick, there are different types of contributors. And if this is, I mean, I think all this stuff is kind of important to like be considerate of when you're doing community, you know, transitioning users to advocates. So the first one, I kinda chose these words randomly. They don't like, some of them I heard some other places and some of them I just made up so like they're kind of flexible and this is very high level. There's definitely more than these but I'm just kinda giving an example. The first one is your lurkers. It's not a bad thing, it sounds bad but those are the people who basically digest all the content. They read everything, they watch stuff, they may or may not comment, they may not say anything but they are actually absorbing the content. Then you have your commenters, people who comment and like and things like that. So that's like your very minimal types of contributions. I don't even know if I spelled that right but it doesn't matter. We're not here, this is not a spelling bee, okay? But people who give feedback and ask questions and those kinds of things, like people who are a little bit more engaged, that's this category of misspelled commenters. People who make comments, that's the category I gave it. And then the third one, and again, this is high level so there definitely could be more types of personas but this is just for the example of like how to do this kind of building. And then the third one is you have your, I don't know if this came up at the right time, but the champions, the people who are actually actively contributing, you're like highest contributing folks. Generally you know who those people are, they're very eager to like do stuff and be involved. So those are like your top level contributors. So it's, the one thing to like note is that you don't want to necessarily convert your lurkers to contributors and chances are it won't happen. So you don't have to think about it like how do I make everybody in my community contribute stuff? It won't happen, I mean it could, right? But like the chances are it doesn't have to happen that way. The way you kind of want to approach it is you want to minimize the barrier to entry. So like with every level of type of contribution you want to give them one step up further than what they're already doing, right? So like for example, your lurkers, most of the time they just read, they don't say anything, whatever, ask them to like like something or like ask a question or like something super bare minimal that you can get them to do some kind of thing. Questions and comments are great because then they can get feedback and that's like when you can pull them into a feedback loop that's also valuable. And you want to ask them for something very, very minimal. So like your, like people who comment or maybe like things and things like that, maybe ask them to give more specific feedback to the blogs that they're writing or they're reading or whatever, or even publicly sharing it. Like hey, if you like this blog post you should tweet about it and tell the author and this is kind of going back to that feedback loop, right? It's like you want to ultimately use your lurkers to feed into the people who are actually contributing to show them that they're making an impact. So it's this full cycle, right? Same thing with like product feedback, if you're trying to like get product feedback from your community, you want to make sure that it's a full circle in some way. So like whoever is receiving that product feedback, you want to make sure that that circles back and that person feels valuable. There's some other things that I'll get into shortly. But again, just slow little levels more and then more than what they're doing. Okay, so this is another minimizing the barriers entry. This is a story. So I do a lot of observations about like communities that I'm in and how I engage with things and what I do and I pull a lot of these understandings and realizations based off of that. And this is some examples. I don't, any of you guys like do Google reviews like review restaurants and stuff like that. Okay, so you're probably familiar with this. You get a notification. I don't know if you guys can see this, but like you get a notification on your phone.  If you went to that time before. This slide was built last night. How was Stubbs Barbecue? Now in this message from Google to me, they're telling me that I'm important. I'm ranked, oh, okay, that's not, I can't talk to you right now. I'm glad people are calling, you know, makes me feel special. Okay, so they put me in the top 10 of Bar Reviewers, right? So they're like, you're important. Your feedback matters. Like we care, like you're, people care. You're top 10. I don't know how they rate that, but it doesn't matter. And then they also told me that this bar, it says the best photos here get over 6,700 views. So they're telling me that I'm important and my feedback matters. Like I'm in the top of the top of contributors and that this contribution is important to the rest of the community, right? So I'm like, all right, this contribution's important. It's my responsibility to give this contribution to people who actually need it. And then once I do one, I just rate it five stars, right? Then they ask me for a little bit more. They didn't ask me to write a full review and answer all these questions and all this kind of stuff. They just asked me for five star review. I could stop there if I wanted, but they wrote thanks for the tip. So they gratitude, right? So they thanked me. And then they also put write review so like I can add a little bit more. So they gave me a little bit of gratitude and then they gave me the option to take one more step further, right? So it's like inching up the stairs. Then they sent me this. Again, I'm still ranked 10% of, I'm sure you guys all are, right? Aren't we all rated top 10%? You've made one review in your entire life and you're top 10%. So I've ranked top 10% of restaurant reviewers now too. Now in this one, in the second request that they're asking for me, they're asking me to answer quick questions. So it's one step further from like the five star review. Can you answer a couple of questions, right? So they first got me doing this and they're like, oh, thank you so much. You're so important. Then like, you're still so important. And can you do a little bit more than what you did last time?  To where I have no idea, right? But like, I'm getting points to do something. Doesn't matter. And they're like, they're making this into a game. They're like, you're going up and you're higher than you were. You're already 10%, top 10% of contributors and you can do more and more. And then of course in here, they're still saying to me, do you wanna contribute more? You can do just five stars and then contribute more and make a whole activity of it. So I was like, all right, why don't we do that? And then they give me this entire form to fill out with like adding photos. I gotta tell them if it's hand to cap accessible. I don't know if it's a place.  So like if they would have given this to me ahead of time, I might have skipped it. But they gave me very small, you know, you're the best, just give us five stars. And they slowly inch you into like becoming a major contributor. And then at that point, that's when you can take it to another level where you like kind of bring them in as a little bit more of like a high level contributor, right? So like basically what they're doing is they're, first they're showing you what your potential impact is. So they're saying to you, you have the ability to make a big difference in this community. This is a requested thing. People want it and you're important. So the impact is great. So they're already showing me that. Then they're thanking me. There's a lot of gratitude in there. Thank you, thank you for, you know, giving feedback to the community, for making an impact, whatever. And then they show me what my actual impact is, right? Like they'll sometimes show you like, your photo has been viewed 12,000 times. You're like, no one has it. But like, it doesn't matter. Nobody's here to challenge what Google says as facts. But this feedback loop is really important. They're showing me that like what I've actually contributed in the past is valuable. And they're also leveling me up. So I feel like something, I'm growing. I don't know what it is, but there's more points coming in there and I'm growing. And then they also highlight to me the next bigger step of contribution little by little. I can't believe I already did 360 reviews for things. That's crazy. Okay, so motivations for contributions. So this is very similar to like the last slide, but I think it's just kind of over highlighting and of like these are really, really important. Foundationally, you have to have these things in your community if you want people to contribute. Gratitude. And this is thank yous. It's not just from you, but from other community members, privately, publicly, thank yous. Like that has to just be thank you, thank you, thank you. You could even someone ask the question, wow, thank you so much for asking this question. Obviously everybody has to do more work now that you asked the question, but like thank you, you know. Recognition, same thing, privately and publicly. Like you want to recognize people for what they've done. Big and small. Thank you so much for rating this thing or giving the comment or feedback to the speaker. They really, you know, this kind of feedback loop. Inclusion. If you are working on something that could be relevant to another person, include them. So like right now, for example, we're working on like our first official meetup in India in Bangalore and we created a Slack channel and we invited everybody from Bangalore. We're like all the people, and they're not helping us, some of them are helping us organize it, but they're just people on the ground that we know, but we're trying to include all of them, right? So like this inclusion is really, really important. The feelings of leveling up, they should feel like they're on a different, higher contributor level than other people. And then I know there's some controversy around this. People are like oh, oh wait no, this is the same one. Yeah, feelings of impact. I guess my notes are different. Feelings of impact and usefulness and value really important. People have to feel like they are valuable and what they're contributing actually matters to people and this is why the ecosystem is so important. That what you're asking of them is actually going to be utilized and digested and fed back into the loop. This is the one that I was saying is kind of controversial. A lot of people are like oh, swag doesn't mean anything. That's true to some degree. If you're giving just swag away at conferences and stuff, it could be great for whatever, but it's not something that people actually value, but when people earn swag, that's when they value it. Which I'm gonna dig in a little bit more into this because I actually like this earn swag kind of thing. So earn swag programming. So I'm gonna give you guys a story, another story. So I am a plasma donor for American Red Cross. It is not easy to donate plasma because you have to sit there for two hours and they pull your blood, they literally take it out and they put it back in the same arm. It's not pleasant, but I'm AB positive blood type so that's kind of what I have to do. But American Red Cross is brilliant with their contribution strategy. Aside from calling you a million times, let's put that aside, which also kind of helps because you're like, all right, I feel bad, people need it. But that's the thing, people need it. I'm like, impact, that's true though, people are dying. So you guys should all donate blood, by the way. Find out your blood type and figure out what you actually need to donate because if you're AB positive, do not donate regular blood, donate plasma. Okay, so earn swag programming. So here's the story of what American Red Cross did to me. Hey, Kareen, you can earn one of these awesome gifts by donating regularly in 2020. This is an annual thing program that they have going on. This is the entire year I can earn something, okay?  If I donate six to seven times, I get a $15 gift card which seems really cheap to me, but it doesn't matter. I'm like, my life is on the line here. And then if I do eight plus donations, I get this American Red Cross jacket that I will never wear because I dress like this and this does not match my outfit. But when I got this email, I was like, I need this jacket. I was like, I, and I got the jacket, by the way. I don't wear it. I've never worn it once, but I did get the jacket. But I was like, I need this jacket. So you have this kind of annual program where you can ask people where they can kind of contribute on a regular basis and earn something. Like they actually contributed, where they made an impact and they can earn something. But that's not all they do. Then every once in a while, they'll spark it up with a here's an exclusive type of swag thing that's only available for two to three weeks. And this one, it's like a game day thing. I don't know, maybe it was like around some something, something around in September or whatever kind of game that is baseball. I guess that looks like a baseball shirt. So like they'll have like these random exclusive things that are either like, they could either be holidays or around some kind of event or launch. Like maybe you have like a launch for a new product that you're building and you want some feedback on it or whatever it might be. But it's like an exclusive giveaway that's just for this limited amount of time that people can earn it. So you have to kind of like combine these different models of how people can earn swag. And if you have questions about swag platforms and stuff, I've used all kinds. You feel free to contact me. I like put my cards on the table afterwards if anyone has questions. Okay. So there's no title to this slide, but that's okay. I don't even know what the title is. So tell you guys another story. Oh, I do know what the title is. This is about making them feel like they're part of a bigger picture thing, right? So it's not just this little thing, it's something much, much larger. So when I was at Neo4j, we, so it was the guy, graphs databases or like the graphs science like graph theory and stuff was created by this guy in like the 1700s or something. His name is Leonard Euler. His birthday is April 15th. So I decided to make a celebration where we made an unofficial holiday just for our community called Global Graph Celebration Day.  We're not doing it, right? This is very little legwork for us. But you guys can all organize your own events on this day. This is kind of like this exclusive one-off kind of thing. It's a holiday thing, right? And we will supply you with those cool shirts. We'll give you, we have this whole funnel thing of like you can, we'll set you with a unique RSVP link to your event and if your people register through there. I can give you guys, if you're interested in like the real details, I can tell you how we operated this, but we ended up having 60 events in six continents with like thousands and thousands of people. And the cool thing is, is that all these community members, they basically did the advocacy for us. It was all these new people who were organizing events and speaking all over the world. We did send them this little video that they could play and all this other kind of stuff, but like it made it feel, it was actually kind of wild. This is a crazy blog post. If you look at, you could probably Google it. It's a crazy blog post. Like literally we handed out these t-shirts and like everybody's wearing these shirts. Somebody made a birthday cake with a graph theory birthday cake and people were like, everyone was wearing the shirts. It was like, it was wild. And everyone tweeted about it too. That was part of the responsibility, right?  It was really, really cool. Another one that we did is a graph visualization. So like graph databases, it's very backend, but there is some really nice beautiful visualizations on it and it helps people understand what graph databases are when you see the visualization. So for Valentine's Day, I did like V-Day and like instead of V-Day, it was Visualization Day and everybody tweeted a picture of their visualization of their graph or their data model and then if they tweeted about it, they get a cool exclusive Valentine's Day t-shirt with like literally the heart. Neo4j is my data bay, we took that. Which I found out bay means poop in some languages but it doesn't matter. So that's, there's the headline. I think I accidentally added animation on it. So you got to make users feel like they're part of something bigger. Oh, there's like one of the graph Celebration Day t-shirt thing. Okay, so feelings of tribalism. So I saw this really cool talk at the CMX conference a couple years ago and I don't know why, just a lot of the things that this woman said really stuck with me. This is the name of the talk. Jessica Wao, I think her name is. If I'm pronouncing it right. I mean, her dad's her name, but I don't know if I'm pronouncing it right. Jessica, I'm probably pronouncing it right. And she had a talk of like how communities relate to indigenous tribes and I thought this was just really, really cool. And I'm just gonna give you the high level points. I highly recommend watching it just because she like kind of digs deeper into like everything. But, okay, so first is like a sense of oneness. So this is where she talks about like colors and language, making people feel like they belong. Even like initiations, that kind of stuff is like it has this feeling of tribalism, but it can create a feeling of belonging. Kinship is having feelings that are like family-like. So you can create like nicknames for family, like maybe brother in like some different languages, or like some kind of nicknames of what you call all the people in your community that has this feeling of family. Then you have language, and this is common languages, right?  I don't know, for like a neo, for some reason it was like cheers and cheers. Everybody was like cheers. I don't know why, because I feel like that matches more Apache Pinot since it's like named after wine. Also, clear roles. This is actually something that's really interesting to people have responsibilities. So like in tribes, you know, you have hunter, gatherers, and nurturers. Leadership, she said you don't need a dictator, but you do need leaders, and like or some kind of ranking, which also helps for the contribution element obviously, but you should have some kind of ranking. And those people should be like, actually like the guy Michael Hunger, who I showed earlier. He was very good at like leading by example. Like he was definitely a leader of the community. That was awesome. Common Beliefs is another one. Rights and rituals. So like kind of like the Global Graph Celebration Day, they still celebrate it now. I mean, they don't do it as cool as I did when I was there, but they still celebrate Global Graph Celebration Day with the community.  So like bring lightness to it, make it enjoyable. You can do like collective things together. So like even if your community is a little bit more serious, you can always start off with something lighter to like have fun together. But I think this talk is great. I highly recommend it. Okay, finding the small contributors. This is a lot of this stuff is actually like, it's very nuanced, it kind of depends, right? But like a lot of it's probably very hands-on when you start off. And then you could try to kind of figure out how to scale it out based on what works. So like something is, this is an example of someone, something, you know, like this guy works target and you know, he just introduced himself in the chat. And I was like, oh, we'd love to hear more about this use case, right? That's like kind of probably a bad example. I'll give you another example. So we had somebody in this, I was looking for the Slack messages, but I couldn't find it because it's like it was a couple of months ago. We had this guy, Diageo, he answered someone's question. They went into our Slack and they say, hey, what's the difference between Pino and like Clickhouse or whatever? And he was like, oh, we assessed this and we found that Pino is more performant and blah, blah, blah. And here are the comparisons and this is what we found. And he like, you know, just a little blurb of, but he already contributed a little bit to the point where like, he's answering somebody's question, right? So like we already got him that far. So I messaged him privately and I was like, you know, a lot of people ask about this topic. I'm telling him, it is impactful. The community cares. If you wanna share your thoughts and write a blog post, you know, we'd be happy to share it with the community and whatever. And I'm like, let me know if you need help. And he's like, oh, maybe I'll think about it. You know, whatever. And like, he's like, and I was like, let me know if you need any help. Happy to talk to you through it, blah, blah. A couple months later, he just published a blog post and had the comparison of all the different technologies that they, it was amazing. And he didn't even ask me for help. He was just like, I wrote this. I was like, okay, great. But it got a lot of attention and I think it's gonna be one of those like very long-lived blog posts which is really cool. So, but initially you've gotta start off really small and then you can kind of try to figure out how to automate it. I can't tell you exactly how to do it because every situation is different. But, but it can really make a big difference when you do it on like a large scale. Okay. These are the takeaways. I think I probably included most of it. You guys can take a picture if you want to. I don't know. There's also gonna be slides shared afterwards too. But yeah, like when you're building your community, you always wanna think about gratitude and recognition and make sure across the board, anybody who's interacting with your community knows that. Also inclusion, don't leave people out. It's really, really important to include them. Feelings of leveling up, where are they going? What does it mean? Like how can you make them feel like they're more important than they are? What is that? Is that five minutes? Is it 10 minutes? Okay. Not bad. I actually was not sure how long this was. And then again, the community ecosystem, the contributions to feed into the cycle. And you wanna do your best to keep the cycle moving in all directions with the things that you ask. So like, again, like if you have people who are commenting or liking like those lurkers, ideal world is you get them to like actually give a little bit of feedback.  So like this kind of stuff means a lot and it does motivate people to do more. So, and it's also the same thing. It's like if you were trying to get product feedback, you're like, oh, the team would really love this idea and we're thinking about doing this, include them in the conversation. Like maybe someone wants to talk to them and dip pick their brain. People actually love that. Like as busy as they are, they want to feel like they're important and valued and their thoughts matter, right? And then creating a ladder of easy contributions. So like, I can kind of tell you guys about like a program that we're gonna get ready to put together. It's basically like a powered by Apache Pino page where people can do a little blurb about what they've contributed and then little blurb, very small, one paragraph, right? Not that hard to like share your use case there but then you take this content and this person's little contribution and then you feed it into a funnel that then goes into more and more larger types of contributions, right? Maybe people vote on the topic or if there's people who are like to point out that use case, you tell them like this is a use case that I think a lot of people would find valuable and that's how you feed into it. And my marketing person told me to put the slide in there so I'm doing it. We're working on a real time analytics conference since San Francisco in August. It is, if you're interested in real time analytics, it is free to join virtually. Well, it's not a virtual, it's on demand afterwards but it's free if you want to do that and then if you want to come, you can come and party with us and all the real time analytics people. And that's it. That's the topic. My timing was like spot on. Does anybody have any questions? I also live my business card, so like if you want, and then I'm also on the Slack so like if you go to dev.startree.ai and you join our Pino Slack, you could find me in there. Probably takes me like a day to respond, but yes. In terms of conversation, like, that's okay. I think that, so she's saying that her community is quite silent so she's like how can we get them to like do more? Like there was like 15 contributors, I guess, that are like actively contributing. Are those 15 contributors people who work for you? Yeah. So sometimes it could take a little bit, so I don't know your community exactly and I'm happy to like talk to you in deeper detail about this afterwards. But so first of all, I think that it's, you have to kind of come up with something like very, very small, right? So like introductions, for example. And this happened with us too. We created an introductions channel because we realized that it wasn't working well in like the general channel. And we have like a greet bot that's like, please introduce yourself and nobody ever does. And then we hired a new community manager who's like working on my team. She started, her name is Yardan Roka. She's amazing. I have to shout her out, obviously. She's like really, really amazing. But she sends people direct messages and be like, hey, I didn't see your introduction. Like, you should introduce yourself in the channel. And it works. And people start introducing themselves. So like, I know, it's like you wouldn't be like, wait a minute. But I think sometimes like there's a little bit more hands-on touch. And the reason why I was asking if you're 15 people work for your organization is because potentially you can give them some of those duties to like greet people or maybe there's like a connector in there that's like, if somebody asks a question about something, they can like make an introduction if someone is doing something similar or something like that. But like you can ask a little bit more of contributions from them too. There probably is like little things you can do. But again, it's like you have to start off so small. Like can't ask people for like big contributions and maybe nudge them a little bit. But if you want, I'm like, I'm happy to like sit for a little while and like really dig in deeper. Cause I learned when I'm like consulting with people about community stuff, I learned myself. I'm like, oh, that's interesting, you know, collaboration of minds. So I'm happy to like talk with you. I'll leave my cards on the table. Does anybody else have any questions? Yeah, that's an interesting question. She asked if like, if you ever have to like kind of work backwards, like somebody was heavily contributing and then they're a lurker. I feel like that does happen pretty frequently actually, like, you know, especially like when your community gets bigger, there's always people who kind of move back. It also could be like that they stopped working with a certain technology. So then all of a sudden it just like, they're off. If there's things like they stopped working with the technology, it's kind of hard to get them to continuously advocate for something that they're just not working with or if they're not passionate about it. But I don't know, I feel like it would probably be, I think it might be like kind of that same hands-on touch a little bit, but just letting them know that you've noticed that they haven't really been around and like asking them maybe something very specific, be like, hey, you know, I saw this blog post, I wanted to get your thoughts on it or something like that, maybe something that they've already done in the past that you know that they are more likely to do because there's people who like do certain things and different kinds of contributions. Like people were like, we have a guy who's helping us organize the meetup in Bangalore and I was like, do you wanna host it? Just be like introducing people and he's like, I don't do that. I was like, okay. So he doesn't do that. So I'm never gonna ask him to host something. But he likes speaking at it, which is really weird, but yeah, maybe a little bit more of that hands-on touch for like the ones that fall out. You know, there's like a lot of platforms now for like community monitoring to see what people are falling out. But some of it's honestly like trial and error. You kinda gotta like see what works and then just keep trying that repeat thing and then sharpening it as you go. I don't know if you use any of those like monitoring platforms, but that might be helpful to kind of see if those engagements work. Virtual question. Whatever. You guys are gonna give, you guys are so nice giving the virtual attendees the question. Okay, let's hear what the virtual question is. Oh, that's interesting. So they asked about how to replicate this when you're doing it in-house, inside of your organization. I think a lot of it's the same thing. Like, you know, you're making them feel like it's like you have to tell them, like this is something big and we need everybody's contributions. A lot of times when I have tried to make our internal employees do something that they're not doing, I schedule a working meeting, but then they are forced to be there. But I would say it probably is pretty similar because a lot of times like when, like these are like very intrinsic motivations, right? Like why do we do the things that we do in general? It's like we love it.  So I guess it was probably pretty similar. Maybe there could be some maybe clearer roles on like what people can do internally, but asking them what they wanna do. But there's like, you know, there's always people who like just do stuff internally, like we have this guy who works with us, his name is Mitch, and like I saw his post in like a confluent, we work very closely with confluent, in the confluence talk about our event. He just posted it there without telling anyone or saying anything. So I just made sure that I shouted him out.  So it's actually like a pretty similar process. I was really impressed when I saw that. I was like, oh, that's great. And then you know, you have the people who are always answering questions on Slack. And it's the same thing. You have to like call them out and recognize them. In like the company meetings, there's gonna be a meeting that talks about people retweeting things, just so you know, telling you ahead of time. People internally at the company, where we're calling out, these are the people who tweet the most and retweet and like and when, you know, and share and all this other kind of stuff internally. So I think it's kind of a similar feedback loop. Okay. Okay. Yeah. So you mean like when you're like, yeah.  Like you can make light of it. It's like, a lot of it's like, you kind of just have to have fun with people.  Did you see this thing? Like, it's not gonna be bad. You know, like, I think it could be, actually I think it's kind of nice that you have, you don't have to worry that people aren't recognizing. When you have an excessive amount of recognition and gratitude, yeah. Yeah, I mean, if it's like a work structure thing, I think you can, I mean, I don't know how you would break it up, but I think you could do something that could break up the type of recognition that people are responsible for recognizing this person in some kind of way or creating a process behind it, you know? So maybe when you're recognizing somebody, that's also like a chance to get them to do another thing, you know? So like, what would be the process behind it? But usually I think it's like helpful if the person who does the recognition is also the person who asks them to do more. You know, like that initial engager is like, it's usually good if they have. Like, Yarden, for example, like she's been going in and be like, you should introduce yourself. And like, if you were to ask any of those people to like write a blog post, I would send her back to do that same thing rather than like sending somebody else. So, you know, I think that when you do kind of figure out how you're gonna break it up, make sure it's still streamlined and the communications should still feel like warm, I guess. Yeah, this guy had a question.  I mean, I had a lot of failed things too.  Like, and so for me, I usually just drive everything with empathy. I'm like, what makes me want to do something? Like, what makes me want to speak at this conference? And what makes me want to speak at it again? Like, what is it that's giving me? You know, like, they give you like a speaker thing at the front and you get this special tag. Like, one of the things I was thinking about with the tags just like, I was like, this isn't noticeable enough that I'm a speaker. That's something that I noticed that I was like, that's how I drive the empathy of my programs. But I've had a lot of failed things too. Like, I did a, you know, we were trying to get people to answer questions on our Slack when I was at Neo4j. Like, we're trying to get our community to answer more questions. So we created this like ninja program where there was like a leaderboard and like when they were answering questions, it would tally up their questions and how much they'd answered during the week. And if they had this thing, they would get this hoodie and roll out, whatever.  Like it wasn't like largely impactful. I mean, I guess to some degree, it all depends on what you think is success. Three people answering questions is good. But you know, it's always, it's like a trial and error thing. And every community is kind of different. But everything that I do, I drive through empathy. I'm like, how would I feel? And like I try to be honest with myself. Like that's like, like I don't want to tell you that like I'm upset that this doesn't show that I'm a bigger speaker than I am. You know what I mean? But like, but you know, it's like part of the honesty thing. Like you have to like, the badge has to be different.  You get, maybe it's a cool speaker pin. I don't know, you know. Okay, I'm glad that I'm glad that it's helpful. It's like, yeah. Okay, so he asked like if you were to start a community today, what tools would you use? I think it depends on what your goals are and how you want people to contribute. So like, for example, I mean like you have the Apple support community, those are like forums and it's probably structured pretty well because it's optimized for Google searches and then also for likes and things like that because if you're a person who posted a question and somebody answered and you have 150 pluses, it makes you feel really good, right? So this forum style works well. For our community, personally, I think Slack is amazing because it is very instant and it's very warm. But I think it all depends on what it is that you're actually trying to accomplish with your community. Like, I don't think Apple support community is really like a community, but it kind of is because it's an ecosystem, right? You're getting people to contribute things that are essentially feeding back into the loop and making sure that this is the best answer. You know, so like, I think it depends on what you're doing. I'm happy to like talk about it if it's something that you're like, you know, thinking about. Yes, thank you. You mean me? Not my team, just kidding. No, no, just kidding, I was just kidding. I did work with my team to do it. So this is like part where you like kind of make it scalable, right? So like the first time we did Global Graph Celebration Day, there was like a lot of things that we wanted to keep on our own. So like RSVP lists, for example, like we didn't contact anybody. So we told them, we're like, we're not gonna contact them, but we need to get the sizes and all this other stuff. But like, I created a forum where they could register their event. And then once they registered it, we publish it online recognition for like, here are the organizers of this thing. And we published it. And then we gave them this URL that was a custom URL. And then everything else was just automated emails. Be like, hey, we're doing this, here's the video, we're gonna send this shipment out, make sure you, you know, your address is right and whatever, but it was like, I created a process. So like, it was a little bit more automated. And actually worked out. And the same thing with the V-Day thing, it was like pretty simple. I'm like, you know, if you tweet, send us like submit the tweet with your visualization, we'll add it to the blog, which we have like a list like you could go through all the blog and see all the cool visualizations. So like it made it feel like it's part of something bigger, but it was just like a form submission. It's like, you did it, put it in the form, your name, email, whatever, and we'll contact you with like, right now we're using for like a swag thing. We just set it up. We didn't even like announce it yet officially. A store where like we can send people points to be able to earn their swag. And that's really nice because then you don't have to get addresses. You could just literally assign it to their email and then they could just go get it themselves. Really huge difference rather than being like, what's your size and what shirt do you want, you know. So hopefully that answers the question. I feel like I ramble sometimes, you know. It's called Cover, that's C-O-V-V-E-R. It's actually really cool.  So like if you, somebody purchased it in India, they'll print it in India. So that's pretty, it's pretty cool. It is horrible, yeah. So I use them for like, we're gonna be using them for like a lot of reward programs like I was telling you like the powered by Pino page. Like if someone does a little blurb and submits their little tiny use case, then we'll give them points to the store and they could pick whatever they want. But then if they write a blog about it, you know that's the email that they're gonna get afterwards, right. We're like, thank you so much for your little contribution. If you wanna make this into a blog, you can get this hoodie. So I use it, we're gonna be using it for those kinds of things. Anything that we do that's like bulk shipment, like I won't get it from like Rush Order T's or Kodas. I use, I mean, a lot of people are familiar with Kodas. They're pretty popular. Noah's my guy there. I use like for kits and gifts and stuff like that. So like we just did like for our champions, we sent them hoodies like Marine Layer. We couldn't do that through cover. It's also like, it's a brand that is not distributed all over the world. So they can't really do it with the routing thing. But the Marine Layer hoodies I got through Kodas. Like they're very like high quality embroidered stuff. Rush Order T's they do for like bundles of stuff. So like when I did the Global Graph Celebration Day and had to ship out 60 shipments of boxes of t-shirts, I did that through Rush Order T's. So they just like shipped them out in bundles for me too. So, any other questions? No, okay. I'll give you guys my business card. Like leave it on the table if anybody wants to grab it or like schedule a coffee or virtual coffee and we could talk about community stuff. I'm always happy to talk about it because I actually learned when I talked to people about their programming and what they're doing and what works and what doesn't. But thank you guys for coming. I also want to say my business cards are actually stickers, so they have a value. They're not totally useless. Thank you.


Good afternoon and welcome. Welcome to SOX will show mark a review of the QQQ's may do a review to this evening of the spy as well But for right now this afternoon I want to go over the QQQ's because I'm actually long this today and Usual for me to be long the market or short mark doing anything with the market because they usually play stocks or companies that gap I'm in an ETF today and the reason is because I knew today the play was long the play was long today. There was no Bearish gaps that I was enthralled with today. I know in a week before a holiday. You're you have to be very picky with what you do Extremely picky with what you do Okay, you're better off on these times of the year to not train unless something is good Again, this is where the conviction helps you and this whole market. It just screams Conviction is a big lesson for people to be learned with this market, which is what? You got to have the right information You have to have the right knowledge base if you know the right information in the right knowledge base Then you won't be able to trade successfully for any length of time And what I find that people lack is conviction in what they're doing because it all the knowledge base What I teach people my golden gap class is knowledge that knowledge gives you the conviction To take the risk in the market to take the trades now once you have the knowledge You still have to get the conviction the conviction comes from the knowledge though That's how you make a decision couple with action decision with action produces results. The problem is that many many people lack Conviction in anything that they're doing on a strategic level because they don't have a strategy or don't understand what to do And therefore when the wind blows by and says the market is falling or crashing or doing anything They want to go with that wind and if the wind blows by in a different direction to get with that wind And then there's 20 other things that happen And then you're all over the place and you're going long and short the market And you don't know what to do and you have to zero conviction You should have negative conviction so you could you could have negative conviction actually Anyways, the reality is though that the market's still higher and the QQQs this counts as a whole this is holding This will hold today. I did think this would hold I Never said in any video that the market couldn't come down in here the way this did in here and still hold I said the market could come down and if it holds it's still higher and so we'll make a new hot Did I think it would come down in the last week? No, does it matter for the overall look of the market? No, why? Because there's nothing bearish in here and any trading action that signifies to me a change of control Now listen to what I'm saying. This is actually important And I review this today in the room, which is one of the reasons why it is so great for people to be in the room And you miss a lot if you did the class and you're not in the room because I talk about stuff in live time But you learn enough in the class to trade on your own But stuff like I talked about today's extra stuff extra teaching above and beyond it the control in the market here is bullish There is not a change of control To make the market bearish Now could you have shorted the market for a short-term period here and made money to the downside? Yes Was that the right thing to do though? No, why? Because who's in control the bulls are in control of the market the markets bullish There is not a change of control that took place in the drop-down that happened the last week Could you have shorted that and made money? Yes. Yes, you could have but is that the right way to trade? No, no, it's not because any day that happened in here in the last week may not have played out that way I knew could not have determined with a hundred percent conviction that it would have come down the way It did because not everything has to pull into support. That is wrong Okay, and any morning that he got up the market could have gapped up and taken you out and continued to go higher Just like it did over here So the reality is that it's not a good train It's not a quality train to be short this market because the control is still on the side of the bulls There's no change of control here to go from bullish to bearish and it's just not gonna happen Okay, how do I know because of the knowledge that I have in gaps because of the fact that I know how to read price action That's how I knew the market here was along today Immediately immediately. Okay, I saw the market was along today And I knew this morning actually that the play was long and I was trying to find a good bullish gap I just couldn't find anything that I liked But the reality is that this market is higher still setting up to make a new hot before the end of calendar year which is in less than two weeks and still seeing the playthrough for 2015 to be an incredibly bullish year in the market and the market is going to go Some numbers in 2015 that no one's expecting numbers that I'm calling here for the longer term trades for the rally Target today for the market is one of two one of two fifty one of three Dream target in the market today if it rallies is one of four. I'm not saying it gets there Even one of three would be a really great target for the market today one or two was realistic and she got there By the lunchtime period only 60 cents away So the reality is that when you choose, okay to short a Market like this Which people are doing because they have a belief system that the market's going to crash and the belief system comes from the fact That they believe that the market is extended If that's your strategic reason for doing this because you're trying to pick a top You can take a trade and make money having shorted the market the last week But it's not going to have any follow-through and it doesn't have any follow through and it will not have any follow through There isn't a change of control and in any day that you're short the market overnight You get up you could be completely blown out of it and that has happened. It's happened to play that already So it's the play in here is long Because the market's higher and the market isn't going to crash and there's no Justified knowledgeable credible reason for anyone to be calling this market to crash The only reason people are saying that is because they're saying they think they believe the market's extended But it's not extended. There's nothing here. Actually that is showing Extension to me people misread even price action when they see Extension people don't know how to read it and why why why why because people are focusing on the wrong information How am I able to all this like this because I'm focusing on the right information? And it's in the price action of the gaps and I know when something is bullish And I know when something is bearish and I can tell who's in control And I can tell who's in control which tells me where the power money is and the power money is what moves stocks in the market And the power money lifted the market today will carry the market over the high again And we'll lift the market in 2015 unless I see Something that changes that which I do not see which is not here now I cannot possibly call this Anything in here Nothing looks like a crash Nothing looks anything like a crash in here is going to happen and nothing looks like a top Okay, and there is no such thing as a top anyways because that's not a strategy There's no strategy There's no strategy the strategy I train is gaps. Okay, so I rent the gap down today to hold The market is bullish. Here we go. Here we go. Here we go. We're gonna hit up over one or two It's gonna fly over that one or two fifty here it goes here. This market goes right here. This is bullish Activity this is buying this lifting the market the market would not be doing this on a gap down unless the market was being bought And that's the other thing where this this is really skilled or read this whole market here That's so higher real skill and it's still that I have it's a skill that I have you can learn from me You can learn this from me. I teach a class Do you if you don't if you don't if you are so if you don't have conviction if you don't know the right knowledge You'll be swayed by anything that happens one red bar. You think the markets crashing one video you watch on TV You think the markets crashing you any much ten and you really think the markets gonna come in you You you know the knowledge that I focus on I stay true to I'm I'm in integrity with what I know and That's I make the calls and follow through and I don't get swayed by something like this Could I have jumped in the bang-bang when everyone else is the markets going to crash? Yes, could I've said it in here? Yes, did I say it in here? No, I said the markets gonna hold gonna hold the hold the main new height It did I'm saying here the markets gonna hold gonna hold gonna hold and many new height is going to I know how to read Priced action in charts and the market and that's how I'm calling these things before they happen I'm seeing the follow through the control is on the side of the bulls That's how I know the market is higher if I see a change of control. I will know it in the moment but that's not happening here and so It's not But I think one of the things a trader struggle with is they don't know what to do So they're easily swayed. They don't know what to do why they don't have the right knowledge base or information Of what they're supposed to be reading But you get that for me if you take my class that knowledge gives you the conviction Okay, and my heightened Conviction and intuition which I focus on and stay true to allows me to see things far into the future and in advance and I'm continuing to do so and That's how I'm calling the market hit some of these numbers that it's never reached That's how I'm calling stocks to do things that No one else is that time calling the entries and I'm calling I'm calling entries and things in the first couple minutes of the day before it's even set the trend of the day And I'm calling an entry in something and I can determine the direction of bias I'm what a stock of the markets going to do in the first five minutes of the day before it's even done anything or said even in a One-minute trend. How am I able to do that? I'm able to do that because I'm reading the gap. I'm reading the gap I'm reading the price action of the gap bullish bearish if it's gonna buying selling shorting I'm reading it and you can learn how to do this from me Many many people train Successfully because they have a lack of conviction in what to do no strategy Don't know how to re-control and are swayed by many things that are out there that are false And many many things are out there that people are guessing like guessing that the market's gonna crash so Everything still looks fine Market didn't have to come down to this level But it did Market is holding this level and it will market will rally today 102 is the first number It's actually gonna get there 100% conviction and we'll see where it goes from there Probably a 50% retracement of the bar from yesterday at the very least which will be 102 25 ish earlier abouts and A lot of people in the works coming all the way down here A lot of people think the mark is crashing a lot of people are short this market And I said the shorts aren't gonna give up on shorting this market Even if it's new high people will short it, but the shorts aren't gonna give it up until way into 2015 Like it could be the summer even the summer the summer of two that it could it could be the summer of 2015 before the shorts give it up and stop trying to short the market Literally, which is so long away and they'll have missed all the opportunity to buy in here They don't go long people Who controls the market power money power money controls the market power money control stocks They sell things they buy things they short You have to know what to read to do in the live day if you want to make money as a day trader And if you want to make money as a swing trader core trader You still have to know what to do you have a little bit more time to think about it But you still have to know what to do and actually more time to think about something doesn't necessarily mean you're gonna see it Any clearer any better because sometimes people take a long time to think about something Can't even make a decision if the wind blows by you and it changes your mind and swings your decision on something You have zero conviction or negative conviction and you will not be successful as a trader You've got to have the right knowledge base. I teach that in the Golden Gap class and on top of that I'm teaching people how to have conviction and by golly. I have conviction the markets higher and the market is higher And this is an amazing call and a great call and it is going to happen and play out and the reason I know this is because I am in touch with what is happening in the price action in the market And I know how to read it and I stay true to myself And I'm not swaying when the wind blows by me and every one of the appliances the markets gonna crash and it's not higher I know that that's not true And I'm staying true to myself and I read it every day and I double-check what the information the knowledge they're reading the price The price action the gaps and as long as I see everything the way that I've been seeing it and give me the confirmation I know that it's going to continue to play out this way And if I see something different I will absolutely say it because I'm honest with myself in my reading and again In reference to my business model if I thought the market is going to crash I tell everyone in the world to short because I love to short myself, but this markets along I'm on the market today, and it has a potential to go to the dream target and here we go We're heading up to 102 So if you're interested in taking the next Golden Gap class, it's in January January 2015 there's no more classes this year But I am running some specials between now and the end of the year if you do want to sign up for the Golden Gap class In January pre-register. I'm offering some specials. So check the emails this week email me if you want to know them Okay, Melissa at the stocks which calm have a great day everyone Have a fantastic day and learn how to trade to learn the right knowledge. You can have conviction of what you do It's the only way you will consistently make money as any kind of trader Have a great day


What's one of the number one reasons why trainers fail? I think point blank. This is the top, top reason is that they can't sell because a trainer in essence is a salesperson because that's what they're trying to do. They're trying to teach you and coach you and sell you on how to make these profound, these, these difficult to make profound changes. It's not that you don't like sales. It's that you're not good at it, which most of us aren't when we first started, most anybody else, they got good at that craft. They had to practice it and they went through a period of sucking and most people that hate it are hated in fear of the work and fear of I've got to put the practice in and it's going to be tough. And I am going to fail and I'm going to get embarrassed and I'm going to say the wrong thing. It's like, you got to get past all that and you got to put the reps in. And then over time, I promise that if you put the work and even if you're not this, you know, like huge personality and charismatic, like that you can get to a place where you can use a lot of these effective tools to be very good at what you do.


Public knowledge has been busy over the past year, busy calling for change from Congress, busy advocating for consumers, and busy protecting users as they navigate the Internet. We've shared dozens of policy proposals and written letters to encourage greater accountability for dominant digital platforms. So I urge you to both press enforcement at the agencies, update the laws, but add new powers so that we have the right set of pro-competition tools to drive entry into these digital platform markets. I hope that platforms will choose to be open and deal fairly with the companies that are using the platforms. Choose to be interoperable, choose to make those APIs available, stop shutting down the adversarial interoperability attempts. Don't discriminate anti-competitively when you are the recommendation algorithm. All of these rules that we're thinking about, they could start following them now. We've spoken up for small businesses struggling to survive online even before the pandemic. Congress must set rules of the road that protect small businesses from anti-competitive abuse and provide the stability necessary for investment and for commerce to thrive. And our experts testified before Congress seven times, published five papers, and filed eight amicus briefs in the highest courts. And when COVID-19 changed all of our lives, our work became more important as policymakers. And the public rediscovered issues that public knowledge had consistently championed, such as open access to knowledge and information, and affordable access to broadband for all. The pandemic didn't shut us down. It accelerated the importance of our role. Public knowledge continued to connect key stakeholders in industry and public interest to find consensus. And we began hosting online events to connect the public to the policy issues facing them in these unprecedented times. It's not just that everybody needs broadband to participate, it's that society is a whole benefits when everyone is connected. In about 10 years since we passed or since the FCC created the national broadband plan, and we've been talking about getting the entire country connected to broadband for many, many years, not just that decade, but even before that. And so to see, you know, this issue raised up as important in this crisis just shows us how much further we have to go. The pandemic has introduced this crazy paradox. People are turning to their local journalism outlets more than ever before for reliable, deeply local information about how the virus is impacting their communities. And they're also using it to counter the misinformation that they're seeing all over the internet and in social media. But at the same time, shelter in place orders and shuttering of local businesses have cratered local advertising. In the midst of important social movements, we showed how systematic policy changes could make things better for everyone. In order to actually fix the problem and ensure that broadband's deployed universally across the country, you know, we need to make sure that every community has access to quality service and affordable rates. We advocated for creating comprehensive privacy legislation to protect Americans online, including their data collected in contact tracing apps. How to prevent this from becoming some dystopian nightmare is that there needs to be controls on how the data is used and there should be three basic controls that we're seeing. One, only collect data that's absolutely necessary. Two, only use the data for what you say you're going to use it for and not share it with anyone else. And then three, delete it once it's done. The problem here is we don't have a federal privacy law, so this all has to come from written agreements with tech companies, with application developers, with governments. What we'd much rather see is these principles enshrined in law. And we've helped protect free speech online, ensuring that every voice can be heard during powerful moments to bend the arc of the moral universe towards justice. The internet is how we bear witness. It is how we see with the hope of understanding those whose experiences, whose struggles are not our own. It is how many Americans were first exposed to the tangible reality of police brutality and systematic oppression. It is how the work of community activists and organizers is amplified and how injustice is brought before the eyes of the world. If we are to strike any sort of new balance, it must keep the needs of 229 million voices and their ability to speak at front of mind. 2020 has made everyone examine how we can help each other, including those of us at public knowledge. And although none of us could have predicted what would happen this year, we've worked hard to meet these new challenges. We are so excited to be celebrating with everyone today, even if we can't be together in person. This year has sparked immense growth and change in our organization and we're better positioned than ever to tackle the challenges of 2021, our 20th anniversary. We hope you'll join us along the way. Thank you for your support.


Today we're going to see how to generate random variates in a simulation using Monte Carlo methods. As you know in simulation we have to have a way to generate values from a particular random variable distribution and the way we do that is with Monte Carlo sampling. This numerical technique goes back pretty far. The name Monte Carlo was the code name applied to a piece of the Manhattan project that was top secret and involved these techniques. In fact the increasing popularity of Monte Carlo methods is what spurred the stimulus for the development of pseudo-random numbers and pseudo-random number generators that we talked about in the last lecture because there was so much in terms of using Monte Carlo sampling it totally exploded and using real random numbers from on a magnetic tape or entered in some way into the program that was used to generate the sampling methods just wasn't going to cut it anymore. It ended up being too inefficient and so it was actually the popularity of Monte Carlo sampling that caused all the work that's been going on in pseudo-random number generators. We know that the word simulation is sometimes used interchangeably with Monte Carlo sampling but in this course and in particular in this lecture I want to maintain the distinction between simulation and Monte Carlo methods. Simulation is experimenting with a model of version of reality and Monte Carlo methods are a particular branch of mathematics and it's a mathematical technique used to solve mathematical or statistical problems and specifically it's a numerical technique, an algorithmic technique. The term Monte Carlo simulation actually is a distribution sampling. It uses repeated sampling from the distribution of interest to determine properties of some phenomenon, well probably because we're going to be summing or getting an average, getting parameters, getting estimates of the distribution. And as we know simulation is a broader technique and especially discrete event simulation which is what we're studying in this course involves a time element and is definitely distinguished from Monte Carlo sampling which is a moment in time. It's a cross-section but a moment in time that doesn't move over time. It's a distribution that's being sampled from repeatedly but the distribution doesn't change. Sometimes the term Monte Carlo is used in a sense of employing randomness or probabilistic activity in order to solve problems that might be deterministic in principle. Sometimes we might know the distribution and therefore we can sample from it but if we want to solve for the mean, the parameter of the distribution it may not be possible or it may not be easy to do it using expected value like we would when we can do it. So if the mean is intractable it's very easy, get an estimate of the mean by many, many, many repetitions of sampling from the distribution of interest and then summing them up and dividing by the number in the sample just like you do it in any field test. We could call it a probabilistic and numerical approach to solving something that should be solvable analytically and actually one of the earliest uses of Monte Carlo methods was to empirically get the approximate value of pi and of course today in starting back from the advent of large computers Monte Carlo methods have been tied to computer programs unlike the historical Monte Carlo methods in the 1700s let's say in the 1800s. These are some examples that are trying to show you a distinction between simulation Monte Carlo methods and then Monte Carlo simulation where simulation is said to be drawing one pseudo random uniform variate on zero one to simulate the tossing of a coin, one coin. If the value that you get is obviously it's a value between zero and one if you get a value less than or equal to 0.5 let's say the coin is heads the value is greater than 0.5 let's say it's tails. This is definitely a simulation and we've done things like this in class but it's not a Monte Carlo simulation. Now Monte Carlo method might be an example of that might be let's take a whole box of coins, pour them out and then figure out the ratio of heads versus tails and that might be a Monte Carlo method of determining what happens in repeated coin tosses but it's not a simulation it's repeated sampling. A Monte Carlo simulation perhaps drawing a large number of pseudo random variables from the interval from uniform zero one assigning values less than or equal to 0.5 as heads greater than 0.5 as tails and it's like repeatedly tossing the coin. Personally as you know I wouldn't call it a Monte Carlo simulation but rather Monte Carlo sampling and we use it in simulation all the time but I got this from Wiki Wand and I wanted to be true to the source. Alright so let's learn about Monte Carlo methods. These are techniques that we use when we want to generate data. What do we need for that? We need a random number generator and we need the cumulative probability distribution for the distribution that we want to generate these values from. We assume in this endeavor we assume that we have a source of random numbers that come to us in uniform between zero and one. We've got this stream of uniform zero one random numbers. It exists, it's usable, it's not going to break down. That's the assumption all of this is based on. Where do we get the random numbers from? A table of random digits, a roulette wheel, some kind of probabilistic activity more than likely today from a computer program, an app that's going to generate these random numbers which as we know because we've already studied them are really pseudo random numbers. To illustrate Monte Carlo methods we're going to use the inverse transform technique. It's easy to understand, easy to demonstrate. It may not be the best technique around, especially in terms of efficiency but it definitely works and it's easy to understand and easy to explain. First, you need the cumulative probability distribution function like the graph that you see on the slide in front of you. You use your random number generator to get a random number between zero and one.  Use a random number generator and a uniform, apply a uniform zero one distribution. And you can see the blue lines on that graph. Well, a random number between zero and one would be a value on the y-axis. Wherever that lands out, we hang a horizontal line to the curve and then hang a vertical line down so that then we can pick out the value of x that corresponds to that uniform zero one random number. Very, very simple, easy to understand process. The next step is that's x. That's the whole thing, x is the sample value. And then you repeat over and over again until you have the sample size that you're interested in. So here's how we would use the inverse transform method to sample values from the exponential distribution with a particular parameter. The cumulative exponential distribution is on the graph in front of you. Again, the vertical axis is f of x, or in other words, a number between zero and one. It's a cumulative probability distribution. It's going to be a number between zero and one. And the x-axis is values from this exponential distribution. Maybe it's times. Maybe it's interarrival times in your simulation. The formula for the cumulative distribution function of the exponential distribution is listed there, one minus e raised to the power of negative lambda x. And this is, so how do we figure out x? Obviously, we don't want to do it with graph paper. First of all, we won't be as accurate as we could be. And secondly, well, we just don't want to use graph paper. We will want to manipulate the formula in order to be able to solve for x. That's the objective, solve for x. We enter this algorithm with a uniform zero one random number and we exit the algorithm, the output from the algorithm is the value of x and then we go and do it again. So the first step is that's the cumulative distribution for the exponential. The second step is to take the one to the other side. But if f of x is a number between zero and one, then one minus f of x is also a number between zero and one. So that's where we put the random number in. And now the random number is on the left side of the equation. The right hand side is pared down to just e raised to the power of negative lambda times x. And step four, step five are all intermediate algebraic steps to turn everything around and just solve for x. And we do that in step six. And now we have something we can use for repeatedly. We're coming in with a stream of random numbers between zero and one. We want to generate a stream of exponential random values. So each random number that comes in goes into that formula and out comes, voila, out comes an x. This is to remind you of the relationship between the Poisson and the exponential distribution. The Poisson is a discrete distribution. The exponential is a continuous distribution. And we run into these a lot in discrete event simulations. Suppose we know that on average four customers arrive at our system, whatever it is, per hour. Well, that's almost exactly fits the definition of a Poisson process. Discrete events in a continuous interval. So this four must be lambda, the parameter of the Poisson process, which is not a function and doesn't change. It's a stationary Poisson process. We look at the units. If the units on lambda is customers per hour, then that works for the Poisson process. If lambda is four, then one over lambda is one over four. And the units on that are hours per arrival. So the average into arrival time is a quarter of an hour, 15 minutes per arrival. That would have to be the mean of the exponential distribution. That's why generally, especially in simulation when we use the Poisson and the exponential so much, we'll often use different designations, different notation for them. And we'll call lambda the mean of the Poisson distribution and mu the mean of the exponential distribution. But the notation is not uniform. So you really just take a look at the units, listen to the words. You have to know what's being talked about here. In this example, we're using the inverse transform method to sample from a distribution that's discrete. That's a customer arrival distribution. And it's an empirical distribution. In other words, we're just using the data as it is. And we're calling that the distribution. We've collected some data and we found out the proportion. We found out how the data is distributed. We're not giving it a name. We're not trying to fit it to any theoretical distribution. We're just using it as is. So here in this case, customers arrive and these are 10 minute intervals. We have a probability of .4, 40% chance of getting zero customers in any 10 minute interval, 25% chance of one customer, 20% chance of two customers, 15% chance of three customers. That's the distribution. It's a discrete probability distribution where we're enumerating, listing the possible outcomes, the probability of each outcome. And in this case, because we need it, we're also indicating the cumulative probability where we just add one to the previous one. The probability, the cumulative probability of zero is .4. The cumulative probability of one includes the probability of one and the probability of zero. So it's .4 plus .25 is .65 and so on. So the cumulative probability of three includes all of the other probabilities. And that's the totality, that's one. With this discrete empirical distribution, the cumulative distribution looks like steps. And that's typically what you'll see. But when you plot it out, the x-axis contains the value, the x-value, number of customers arriving. The y-axis is the probability, the cumulative probability, so it's a number between zero and one. And we can do the same thing. If you use the inverse transform method, you generate a random number, uniform zero one, figure out, look at it on the graph, and horizontal line till it bumps into the curve, then hang a vertical line to get the x-value that you got. So for instance, if the random numbers that we generated are .09, .54, and so on, well, for .09, anything between zero and .4 will be zero. So that's a zero. In the first time period. In the second time period, .54 gives you a one. .42, slightly above .4, also gives you a one. In the fourth time period, we get a .8. And that matches the x-value of two, two customers arriving in that time period. And then in the fifth time period, we go back down to zero. And so we've pretty simply used what would the exponential look rather complicated, but in this distribution, since it's discrete and we're just looking at a fairly simple distribution, it doesn't present any intellectual challenges for us at all, at least I hope not. But we're going to look at something soon that will give us a challenge. All right. It's one of our favorite distributions, the normal distribution. We know so much about it. It should be easy as pie to sample from the normal distribution and generate normal variants. Let's see. First of all, before even going further, we're going to forget about the normal distribution and stick to the standard normal. Because it's been studied. We don't need to derive any formulas. We don't need to create it all over again for every single pair of mu and sigma. The standard normal is usually called Z. Z is distributed as normal with a mean of zero and a standard deviation of one. Great. But of course, that's not really what we want to generate values from. Still, if we can generate the Z's, that's great because we could take any Z and transform it back into an X, solving for X again using algebra. I guess that's a side note so that just to say when we're talking about the normal distribution and sampling from a normal distribution, we're really talking about the standard normal because it's a very easy transformation to go back and forth between what we'll call X and Z. The probability density function for the standard normal distribution is given in the middle of the slide. It's rather complicated, but it's not that terrible. It's 1 over the square root of 2 pi times e raised to the power of negative one half times X squared. The formula for the cumulative probability distribution of the standard normal is a little bit more complicated but it's not something we would really want to work with algebraically to solve for X. In fact, it's pretty frightening.  Again, using the graphical approach is very inefficient and time consuming and it's hard to generate a computer program to do it. So do we really want to use the inverse transform method here? Probably not. Thankfully there are a lot of other alternatives. I'm going to show you one on the next couple of slides. There are different methods that are used for sampling from a normal distribution. Here I'm going to present to you one that's usually called very simply the sampling method and you'll see why pretty soon. It's an easy to explain method. It's an interesting one to look at. Probably not one that's actually going to be used because it's not terribly efficient. We'll look at some of its deficiencies after I show you the technique. This method is based on the central limit theorem. So recall the central limit theorem says that sums are averages of distributions that are not normal. As long as they are symmetric they very quickly become come to look like a normal distribution as the number of items that you're summing, the number of variables that you're summing together as that number gets larger and larger and larger. So here's look at this example here. We're looking at a very, very simple probability distribution tossing a die. When you toss a die you can get outcome the number that's on the face of the die either a one or two or three or four or five or six. They're all equally likely. So the probability of any one of those outcomes is one six. That's a typical rectangular distribution and it's a uniform distribution. But what happens if we toss the die twice and outcome we're looking at is the sum or the average of the two outcomes from the two tosses?  Well it so happens that in the first case you will start ending up with a rectangular distribution. And a rectangular distribution is not that much different from the normal. It needs some smoothing out but it's certainly symmetric. The mean is equal to the median is equal to the mode and so on. But what happens as you toss the die more and more times and accumulate the sums over that number of times? This distribution does in fact start to look very much like it has a bell shaped curve. Well as you know it's not enough just to know that you're creating this normal distribution by sampling from let's say a uniform distribution. But it's nice to know you can do that. But you also have to know what the mean and the standard deviation is because what we really want is the standard normal distribution. So we at least have to be able to figure out what are the parameters of this normal distribution that we're counting on having sampled because we're summing the values generated from a uniform zero one distribution. Well as far as the mean goes for any uniform from A to B distribution we know that the mean is one half A plus B. So for the specific case of the uniform zero one the expected value or the mean is going to be one half zero plus one or one half point five. We know that the expected value of the sum of two random variables is the sum of the expected values. The expected value of x plus y is equal to the expected value of x plus the expected value of y. And by extension if we have more than two random values from this from these random variables then we can add those as well. So the method goes like this let's say we have 12 what would happen if we have 12. Well for random number from a uniform zero one distribution the mean is point five and one half. So what happens if we have 12 well it's one half plus one half plus one half 12 times. So in other words the mean will be six if we sample repeatedly 12 times from a uniform zero one distribution will have something approaching a normal distribution. We'll have an approximation of a normal distribution with a mean of six. Now what about the variance using the same tools that we did for the mean the variance of a uniform zero one distribution reduces to one over 12 one 12. If you when you sum variances or when you get if you want the variance of a sum you can also sum the variances just like we did with the mean and that's a nice feature. So for two it would be two times the variance for 12 it would be 12 times the variance. That's one good reason for using 12 12 times one 12 is one if the variance is one the standard deviation is one and we're halfway to a standard normal distribution. Finally here's where we draw it all together. What's the actual process for using this sampling method to generate values from a normal distribution. Well the first thing we do we start with our typical uniform zero one generator. We get 12 of those add them up and then subtract the number six. Why because we need the mean to be zero. The variance is already zero the standard deviation is already zero. So once we're finished with step two. We have a value for generated from the Z distribution the standard normal with a mean of zero and a standard deviation of one. Step three is then simply using the transform algorithm to go from an X from a Z to an X using whatever the parameters from the normal distribution that we're interested in that we started out with. And that's that's it it's done it's very very simple it's not great but at least it's simple easy to do easy to understand. Okay so what's so not great about it well the fact that we're limiting ourselves to 12 summing 12 random numbers in order to get value from a normal distribution. Even if it's a decent approximation where we're limiting the values that it can take on and sometimes we do want to sample from very low probability values in the extremes. And this won't be very amenable this method won't work very well for that. And in addition I mean really 12 random numbers for every normal random variate. We're going to run through our random number generators period very very quickly so then in addition we need a pseudo random number generator that doesn't start cycling too quickly. What do we use all of this for in simulation. We use this in order to generate values to that are used as input to the simulation. If we have customers coming into a bank we need to generate into arrival times we if we have a machine shop we need to generate the time until the machine goes out of service for whatever reason. So these are the inputs to the simulation. This all assumes that we know the distribution we want to sample from and that's a whole other lecture and that's what's coming up next.