So without further ado, I am going to share my screen. So I can't share a single window, I have a problem with you.  Okay, so do you see my screen? Yes, we do. So we're going to put full screen if that works. I thought it was this way. Anyway, let's keep this presentation this way. That's fine. If that's big enough, or that's not big enough, tell me. So, yeah, I wanted to make a quick update of the Guava work. You know, that was started some times ago. You may have seen, if you didn't, that's okay, because I'm going to explain again some updates here and there on the developers mainly, and so on, on some various efforts around basically being able to upgrade Guava in Jenkins Core. So in Jenkins Core, so I looked for an old cat picture. We have, we are using Guava 11. Guava 11 was released in 2012. And the last version is Guava 30. So we want to upgrade for various reasons. One main reason is security de facto. If we see if someday, you know, there's a CV that's discovered on Guava, old version, and we may be vulnerable. The Jenkins project may be vulnerable. And then upgrading, fixing will not certainly be easy, as you can imagine, because this is very old and nobody about, but neither Jenkins project would be able and willing to backport whatever. So this is a problem. So we'll start looking into what it would take to upgrade. So there's a JEP ongoing that was started by somebody else than our team. So because our team at Cloud Bees has started looking into the bigger picture, there has been a lot of efforts from various members in the community, not working for Cloud Bees. So I created just before the computer summit an EPIC, because I thought it would be nice to start and gathering things around. There has been a few PRs and so on that were started before. So this is the one I'm going to look into it for now. And then so James Nord on the call right now, I think. So started to look into some months ago, some weeks ago, what would happen if we would upgrade Jenkins Core, the version of Qua-Veinsat Jenkins Core from 11 to 30. Basically, James used the Rave API tool, basically a tool, Rave API, this one that analyzes the API and their backward compatibility and so on. And I did that in the mix using Usage and Plugins tool. That's a tool from the Jenkins community that's going to be scanning the whole bytecode of the plugins of the Jenkins ecosystem to find potential breakages, future breakages. So because going back to my slides, basically what we want to do is to upgrade all plugins to check whether they are working. So I'm going to show you, and it's going to be a good discussion following up the question earlier about the plugin, EOL policy, lifecycle work that some people here were in about the importance of clarifying what plugins we need to fix and the plugins that may be too old to have somebody care about. So this list is the following. This is the plugins that may be impacted by the Quava upgrade. So I'm scrolling, as you can see. A few plugins in that list are CloudBis proprietary because of the way we scanned, but that's most of them are open source. So you can see this is a small project, right? So why am I today talking about this? It's basically to raise awareness because we need the community to participate in that effort. Many fixes needed are a good way if you want to, you know, create your first open source PR. That's probably a good candidate work because most work are going to be, should not be very tricky in many, many cases. I'll explain afterwards what I mean by not too tricky. So yeah, we need people, but I'm going to now expand a bit more precisely what it takes. And you will see it's not rocket science. Any questions at this point? So what does need to be done to adapt plugins to Quava? It's, you know, you're going to look at a given and then you're going to upgrade locally. There's multiple ways to do what I'm describing right now, but that's one way is to basically upgrade locally your POM to force Quava 30. That's not in practice going to be used, but that will be simple and enough to run your tests using Quava 30. If that works, you're good, these plugins will work. And then we can consider this plugin is like, okay, stamped as okay to work when we are lending an upgrade of Quava 30 in Jenkins Core. If it blows up, then we need to fix this plugin so that it works with both. What does mean fixing, which here I explain here, it means that first recommendation is getting rid of Quava usage when that makes sense. If you're using, say, Quava, I don't remember the name, unmodifiable list, probably you can switch away from this one and use the collections.unmodifiable list API for instance as a standard from the JDK. That would be the simplest way when Quava is used, if you're using one utility class or something from Quava. If you can't, then you need to try, you need to make it work with the same code in a forward compatible way between Quava 11 and Quava 30. That means that your plugin, if you're doing nothing, meaning not forcing Quava, and then you will be using Quava 11, and then you force using Quava 30, you run just MVN verified twice, before and after. It should work and succeed the exact same way. When you're in that case, you are good. With the pretty important caveat that if your plugin has no test coverage whatsoever, what I'm saying is wrong, because then you won't see failures, you won't see breakages. But then, if this plugin is missing tests, that may be the right moment to add some, to show that it's not breaking. Then it's going back to usual development process, or maybe using code coverage tooling and so on and so forth, to cover the Quava usages and then going back to the process I'm describing right now. Questions? I was going to be a quick update, so that's everything I wanted to raise to discuss today. So if there's no question, that's fine. I think I'm going to... Is anybody just there? Yeah, not just looking at the right. That's somebody here I'm saying? Yes. Yeah, I was just a bit suddenly worried that I was muted since 20 years. So we're ready for you to start your presentation. Exactly, suddenly I had a small cold sweat, as we say in French. Okay, cool. So yeah, you see it's an easy thing. Just a few plugins to check. So, as you said, the reason why we're talking about this today is that there's something that needs to happen, but also that it's something that is very much parallelizable, right? That anyone can do it and... Yeah, absolutely. Yeah. It's a great opportunity, like for instance, in the Jenkins community for years, we have been labeling some JIRA issues as nooby friendly. I think most of these fixes are nooby friendly. If you're a Java developer, if you're not very much experienced in Jenkins development, this is going to probably be an easy one for you to enter open source, play with it, interact with nice people. We have cookies, and help this thing to move forward. Because basically what we want, I'm going to re-explain that very quickly just to step back. We want to upgrade Jenkins, the Guava version in Jenkins Core. But to do that and not make the whole ecosystem explode, we want to fix the ecosystem first. What about with all the plugins that are candidates to be the precators, applying the policies that we want to apply? All those plugins that are only compatible with 1,400 and this kind of stuff? That's a very good question. So, yeah, something like one hour ago we had a session that was pretty productive about plugin EOL policy and so on. So, I think the example you just gave is an easy one. We don't care. If the plugin only works with 1,400 probably those plugins are already dead de facto. But if a plugin still works on the 2,280 or 90 something weekly, yeah, that's a different issue. To be defined we definitely want to that's part of why we were pushing for this discussion today definitely that James was talking about because I think the Jenkins community if we manage to have a life cycle policy somehow it will reduce the size of the work needed for Guava. Absolutely. Those things are very much intertwined. Also, I ask because recently I tried to break the version of the Apache minor SSHD in the core and we managed to extract the plugin as mobile and we are struggling yet with repercussions of bumping the version and so on. And it's been 7 months or something like that to do a thing it's only one plugin and it has a few dependencies, 10 or something like that. We feel you. I think the thing to be to note here is that creating creating the PRs to make the change is one key step because then you can say look we've done our due diligence and the community has done its best here's the change. If it doesn't get merged there's enough traction in the plugin then you'll have a baby making very interesting noises on your lap. So as long as you've done that then there's a second discussion that you can have that says look we've done this nothing's happening it's time to let that go or someone needs to step up take over that maintainer shape or whatever it's not directly the EOL question but it's one where you can say we've done the work now it's up to whoever cares about this plugin. Yeah, that's what we've done for digester work and I think that pattern is one that we can continue to follow. To be frank I think this is an unideal pattern that's the least worst case or something the least bad way of finding PR but then that means still Liam that you need to spend time finding a PR that probably nobody would attend to. Right, my point here simply that I mean if it's a small PR then great if it's a large PR then maybe it's more problematic but as we were saying this is generally not a hard PR to do. Yeah, most often and if we have a large many hands make light work kind of thing going on then great, if we get enough people like that jump in on this hey if I mean I think that's another point here that that contributorship isn't just I did the work I did the work and it moved this project forward even if that PR does not get merged and I think if it doesn't get merged and someone new has stepped up and said this plugin is important to me so I'll kind of do this that's a step towards kind of getting that plugin maintained it's like hey it's important to me I've done this work I use the plugin and I want to keep me to keep using so it's hopefully a way to then go well this hasn't been merged and you know come to the community to that list and they'll go why hasn't this been merged and we say well you could ask to adopt the plugin if you wanted and become a maintainer of it I guess a number of tools that I've taken on contributorship to not plugins but tools it's like oh well I want to do this one thing oh it needs more help and that's how you that's the onboarding process right so yeah it's I agree it's not ideal but it's something I guess let's stay with this discussion or we can keep going I don't mind but the plugin EOL is kind of a separate subject even if it would help you know it's connected but different subject and you see why it was so important I alluded to that earlier today I did I think we're done it was really I think my next step is just I'm going to choose like one thing and one question somehow I'm going to update maybe send an email to the developer mailing list or something maybe the discourse should create a thread there probably and then the question is like do you think I should create a g-reissue for each of the plugins in the epic I could automate something to do that I'm not going to do that by hand but maybe that would I see you even I agree I was not thinking I was going to spend my evening creating 300s g-reissues so yeah that would that would be helpful but do we have a blog post for this because I think there's some interesting stuff to be talked about with this like hey you know Jenkins has these things and it might be a visibility thing there too because this is actually something that the community you know yeah that's a good point that's even more why you know I would probably want to create a g-reissue for each because then we have a blog entry and then tell people use this feature everything that's easy up for grab and you can assign yourself with the plugins you care about and then it's clear for you or something yeah yeah I'd be up for writing that blog post I'd be that's something I'd like to talk about it's the kind of thing where it's raising the why we're doing this what we're doing why it's hard why it's easy it's an interesting view into the community into the Jenkins plus you know absolutely doing what we're doing right now but at scale because right now we are the group here I don't think a lot of people are going to be watching and missing to that and so on making it believable to you know twitter account of Jenkins and the blog would probably also make the impact way bigger yeah so I've written some actions I'm going to write something on the dev list maybe on this course I will check with all the things the JEP we need to finish somehow but that's going to be midterm long term because anyways we know what we need to do for the plugin style of things create giras for plugins and then write the blog entry about the upgrade for raising awareness and getting hopefully scaling for free for those like hundreds of things to fix thank you everybody


That Sam was as old fashioned as you could get, especially when it came to technology. He refused to own a microwave, a cordless phone, CD player, like living in medieval times.  It wasn't so unusual, holding on to the past, but one thing that always bugged me was that TV of his. My definition was all the rage, but here was Sam with this black and white RCA from the Stone Age. I mean, you had to turn a dial to change channels and there were only 14 of them. I don't even know how he got any kind of signal. He used to say that God kept the shows coming. Maybe he believed the spirit of his dead wife, Agnes, was beaming cable down from heaven. Come to think of it, this technology business all started when she died. Makes sense, I guess. The loss of a loved one can change us in odd ways. I think Sam wanted to stop time, or go backwards even. But there was never any sadness there. It must have been about respect, respect for things that had gotten old and were being forgotten. I'm sorry I ever stepped in to fix what I thought was broken. 2009 rolled around and the time had finally come for standard definition to take a hike, but Sam was completely out of the loop. They're switching everyone over to HD. I told him. You won't be able to watch TV anymore unless you do the switch. I don't know if that was really true, but Sam said it wouldn't matter anyway. I tried to get him to call the cable company and talk to them about it, but he insisted he didn't have a provider. I asked him where his cable bills came from and he just looked at me. Maybe I was overstepping as a friend and neighbor, but I honestly thought I was doing the man as service. Would he be happier with crystal clear color on a big screen? Twenty years ago Agnes died. Twenty years was long enough.  Time is different for people like Sam, people who've lost their spouse but have to go on living. The same thing happened to my dad. It's no wonder I never married. Every year, Sam went fishing with his brother for two weeks up in Maine. Being his most trusted neighbor, I had a key to his place in case of emergencies.  I called up the cable company, posed as Sam and had cable installed in his house. I even bought him a brand new 32 inches television and had them put the bills in my name. Sounds like a good deed, right? Totally illegal, but a good deed nonetheless. We all thought it was brilliant and exciting, imagining Sam's face when he would walk in and see the future had dropped right into his living room.   I placed his beloved hunk of junk right next to that thin black beauty for a nice jigs to position, the old and the new, side by side. I knew he wouldn't be able to resist at least trying it out. Sam returned late one rainy night from his fishing trip. I'd been waiting up so I could see his reaction, but I was dog-tired by that point. I looked out my kitchen window into his living room. The TV wasn't visible but I knew it was on from the reflections on the glass. Man, I so wanted to call him and yell surprise. But it was more funny imagining what he must have been thinking. Maybe he thought God did it. I waited for something to happen. Was he going to call and accuse me or thank me? The phone never rang so I assumed he didn't want to wake me up. I wondered if he'd called the police but nobody showed. The waiting was driving me nuts. If I hadn't been ready to conk out I would have gone over there. I wish I had. Early the next morning I phoned him up. It just rang, no answering machine, so I went and banged on his door. I could hear the TV but nothing else. It's not like I couldn't go right in but I sensed something was wrong and I just wanted Sam to come and tell me everything was okay. I figured he knew it was me who orchestrated the whole thing and that he was just angry. Apprehensive as all hell, I went in, leaving the door wide open.  It sounded like one of those slasher films. I didn't recall Sam being a fan, but with over a hundred channels he was bound to stumble across all kinds of garbage. I called out his name from the front hallway as I cracked toward the living room. When he didn't respond, I thought he might have passed out from watching TV all night. But then I noticed his old RCA had fallen onto the floor, face down, not a good sign. As I gently lifted it back onto the table, there was Sam's body laying right next to it. Facedown as well, he had one hand clutching his heart and the other reaching for the something, probably the TV, but with the way he fell I'm not sure which one. I quickly turned him over to check his pulse. Needless to say, he was gone.  It's not something you forget easily. After the cops showed up, I spent a lonely night in jail. No charges were filed. Yes, I was technically a criminal, but the coroner said that Sam had died of a heart attack. Must have entered into Jesus, scared out of him by something. He suggested. And with Sam's age and apparent heart condition, well, you can see where this is going. I guess high definition is just too real for some people. Although, in retrospect, knowing what I know about the man, there could be more to it than that. I still have Sam's old television up on a shelf. The screens cracked a little but the picture's okay. Sometimes, I could swear it turns on by itself when I'm not in the room. Maybe he's trying to tell me something. I just go up to it and say, sorry buddy, and give it to lightpats on the side. I mean it too. I'm really sorry Sam. I guess you're with Agnes now. Make sure to keep the shows coming.


Live from New York City, it's theCUBE at Big Data NYC 2014. Brought to you by headline sponsor, Juan Disco, with support from EMC, Mark Logic and TerraData. With hosts, Dave Vellante and Jeff Kelly. Welcome back to New York City, everybody. And we are really pleased. We're going to dig into the networking space a little bit. Dave Husak is here. Founder and CEO of Plexi, a company in New Hampshire. And networking is a space that's obviously been dominated by Cisco. The company's got two thirds of the market and has for years. Networking's this big, top-down, hierarchical animal. Compute scales out. Storage scales out. I think Plexi is the vision of making networking scale out. So, David, welcome to theCUBE. Thanks for coming on. Thank you, Dave. I'm glad to be here. So what's the story, right? Like I said, compute, storage. Everything's going to scale out. The network has to go scale out, does it not? It does. It's the element that makes all those other things work. It's for high performance, scale out data, accessibility, and computing. And Hadoop is obviously a fantastic use case, a fantastic expression of all that. And networking is central to making that work. So I want to get into that. But before we do, tell us a little bit about Plexi, how and why you started the company and give us a little background on it. Sure, sure. I've been a networking guy my whole career. Way back when in the 90s, I worked at one of the companies that actually built and installed the first switches, ethernet switches in the world, before we even need to call them switches, right? And... What did you call them back then? Well, actually, Ethernet Express is what our product was called. Back when, you know, it was 10 megabit ethernet and things were connected after the iBackbones and stuff. That was megabit, folks. Yeah, megabits, megabits. Electrons were way slower back then. And so at some level, I helped create the problem that we're now solving here at Plexi. That's what entrepreneurs do. Yeah, it keeps the cycle rolling. But we have basically, with Plexi, the inspiration was actually a lot of what you, the problems that you set up already is that recognizing that the way we've been building switch networks, you know, hierarchically for the last 20 years now, doesn't scale the same way applications and data is scaling out. The requirements have changed. And, you know, 20 years is a good run for a technology and it was time for something different. And a lot of it, so the inspiration for Plexi, we got started with the idea sort of germinated and developed back in 2010, raised our A-round in 2011, followed that up with a couple other, you know, funding rounds and rapid succession. And, you know, we think we have a take on networking for scale-out applications and Hadoop and Big Data and that offers, you know, really compelling advantages compared to the alternative, which not only is Cisco, but is kind of everybody else, right? They all essentially build fundamentally the same kind of product, whether it's leaf spine, three traditional Cisco three tiered course, switches and things, right? They all have this property that, you know, if you want to build wider, you have to build taller, right? And so it's fundamental geometry. You can't get away from that, right? We have a different way of wiring networks. We have a different way of orchestrating networks. We employ SDN as the methodology that glues all that together and delivers a level of automation and visibility and manageability that the other guys can't touch. So I'm envisioning this sort of mesh, this fabric that's sort of controlled by software. I want to get into the Big Data and then we can maybe get into your technology a little bit as well. I remember at Hadoop World in 2010, I didn't know much about Hadoop. I'd read a little bit about it, but when we started to talk to some of the practitioners, Abhimeda in particular, who's the guy we're going to have at our Capital Markets event tonight, said, listen, the fundamental is you ship function, you ship five megabytes of code and not a petabyte of data. And so I said, okay, well, it means tons of data. I get that. It means getting compute closer to the data. I get that. What does it mean for networking, that fundamental notion of distributed computing, function shipping, what does it mean for the network? It's all about agility. It's all about being able to place the computing with respect to the data, with respect to the resources it's going to consume in a way that ensures that it's making, it has access to the data it needs. The data is replicated across the right kind of boundaries to ensure that the reliability and resiliency is there. It's ensuring that one of the things people don't talk about enough because it is a hugely important problem, especially as Hadoop and Big Data application sort of proliferate. But security concerns, right? In some cases, payment card, healthcare, there's a lot of applications out there where there are regulatory requirements that are problems that have been solved in sort of conventional data file systems and processing architectures, but also need to be enforced in big data installations as well. All of these things are mediated historically by big boxes of network functions and firewalls and filters and such that are static, right? Moats that are dug around the castle. Exactly, exactly. And that's sort of counter purpose to the way we kind of now think about employing computing and accessing data in large sets that may be geographically distributed. Maybe my data's on my data, some of your data to actually accomplish a particular application. So the thing that ties all that together can't be static. It has to be agile. It has to be fluid. And networks need to evolve out of sort of a rigorous hierarchy that's defined. Networks of today are effectively defined by where the wires go, right? That's no longer optimal. It's no longer practical. Okay, so everything is virtualized and fluid on top of it. Right, okay, right. It becomes a mess and really from a security standpoint, very hard. So how do you solve that problem, number one? And number two, how do you convince the Cisco certified engineer that they should take a chance on Plexi? Well, hopefully we're making it less of a chance as the product, we are delivering our sort of second version of our products with like a lot of storage. So we're a little over three years old, right? And we now have delivered Rev2, which is, as you know, for startups, Rev2 is the real first product. The Rev1 beta products where the test the water kind of things, right? But first, yeah, it is less of a chance because we are fully interoperable. We've plugged into lots of people's networks, lots of environments. And so the ability to add Plexi, Plexi Agile Networking capability to existing networks is easy. I did actually worry at the beginning about the question you posed, right? Like, because, you know, back then we were telling the sort of the big story, the, you know, what it's gonna be like to have a network that works this way, that software defined and Agile, and of course that narrative is immediately appealing to the CIOs, the application architects, the guys who, you know, the users of the network, as opposed to the guys who build and operate the network, right?  It's been 20 years since we've been basically doing things the same way, right? And they have huge investments in scripts and CLIs, you know, the kind of the archaic ways that networks are built and operated generally today, right? It's their house. It is their house. And so you can't, you know, not in my house, right? You can't just expect them to, you know, to accept something new and different. What I didn't, so we started engaging, you know, like about, you know, as we're delivering our beta products into our first customers, you know, we were, I've obviously had to engage, right? And what was striking was how much of the frustration on the network user side was actually mirrored in the network engineering side, right? These guys knew they were behind. They knew that the guy who was orchestrating, you know, vSphere and vCenter was, you know, can make thousands of servers, you know, spring into existence, vanish, copy themselves, dance across the networks, you know, with keystrokes and mouse clicks all day. And they were the guys that were still, you know, typing cryptic commands into CLIs at 3M on Sunday mornings, right? Which was, you know, the gap between that is just crazy, right? And they knew they were behind. They knew they didn't have the tools. They weren't getting the tools from their vendors that could allow them to keep up. So you're saying they were more receptive to it? They are more receptive. I think the, you know, as we refined our proposition and matured our products, it's now becoming, like I said, hopefully it's not as even scary anymore. It's actually, the advantage is outweigh the, you know, the risk of bringing it a start. Well, it helps too if you're 10x better. Are you 10x better? We are more than, you know, depending on all the axes, you know, we are more than, it's just a different model. It's, in fact, it's, you can do things with Plexi that you simply can't do with other guys. So that's infinitely better. David, we got to leave it there. Get in the side. Thanks very much for coming on. Thank you. Really interesting. And we'll be following you. Hope to see you back into England. Sweet. All right, keep it right there, everybody. We'll be back right after this word from Big Data NYC. This is theCUBE.


Y clytidon ymlaen i, yn'r geigffordd bywydeth, the next item of business is consideration of business, Motion 2456, in the name of George Adam, on behalf of Parliamentary Bureau setting out changes to today's business. Any member who wishes to speak against the motion should press their request to speak button, now. I call on George Adam to move the motion. Thank you President and I moved. No members asked to speak against the motion, therefore the question is that motion 2456 be agreed. Are we all agreed? The motion is therefore agreed. The next item of business is topical questions. In order to get in as many people as possible, I would prefer short and succinct questions and responses. I call it question number one, Jamie Greene. To ask the Scottish Government what resilience measures are in place to tackle serious organised crime and terrorism in light of reports that the assistant chief constable in charge has been suspended. That is an operational matter for Police Scotland. The chief constable has confirmed that the assistant chief constable, Tim Mayers, will move from his current role on an interim basis to take responsibility for the organised crime, counter-terrorism and intelligence portfolio. The member will appreciate that it would not be appropriate for me to comment further, although an investigation is under way. Jamie Greene. I do appreciate that there is an investigation under way. However, it is the seniority of the individual and the importance of his remit that causes the most concern. The assistant chief constable suspended leads the charge in tackling serious organised crime, terrorism and cybercrime in Scotland. We know that cybercrime increased 95 per cent last year. Web-based grooming offences have increased by 80 per cent over five years and the police are currently investigating nearly two and a half thousand serious organised gang members in Scotland. Can I ask if the cabinet secretary is confident that we are making progress in tackling those crimes and what steps has he personally taken in the past few days to make sure that those recent events will in no way impact Police Scotland's ability to protect the public? Cabinet secretary. As I say, there is not much I can say in terms of the actual investigation. Just as the member says, it is very important because of the level of the person involved in the organisation that it would be just as important for a member at any level in the organisation in that kind of case. Is the responsibility of the chief constable to deploy his force as he sees fit? I have had discussions in the last few days, both with the police themselves and with the SPA. I am confident that the police and the chief constable will ensure that the same kind of coverage, the same kind of effort has been made in relation to organised crime and cybercrime, as was being made before this case came to fruition. That will be affected by the changes that the chief constable has put in place. Jamie Greene I am reassured in the sense that a conversation has taken place about the resilience of the police's ability to handle such serious crime in Scotland. Let's not forget, Presiding Officer, that it has been over a year since Dame Angelini's final report into police misconduct and complaints handling was published. The Government, I remember, snuck out a progress report on the final day before summer recess. I raised it as an issue at the time, but we have heard nothing since. It remains a fact that, astonishingly, an officer can resign while suspended during an investigation with no further action or recourse taken whatsoever. Why is that still the case? That is a very important point that Jamie Greene makes. He knows that it was one of the recommendations in Dame Angelini's report. He will know that there were more than 100 such recommendations, many of which have been progressed. To reassure the member, a meeting took place last week at which the latest tranche of recommendations, which have been progressed, were summarised and will shortly make a statement and make public the progress that has been made throughout the range of recommendations. The one that the member refers to, of course, is one that would require primary legislation to change. It is a question that we will have to take forward that. Perhaps another provision, which is in relation to advisory and barred lists, whereby somebody who is convicted of offence in one police force cannot join another police force without that police force being told about it. Those are on their own two very important recommendations, but they will require primary legislation and, if we take them forward, will require to be fitted into the legislative programme, just to say that justice currently has around 22 bills scheduled for this parliamentary loan before any bills that the member might bring forward and others. It is a congestive programme, but we intend to take that forward seriously. Serious progress has been made throughout the recommendations that Ailish Angiolini has made. I thank the cabinet secretary for that information. He will be aware that there has been an 18-fold increase in the stoppages of so-called street ballym in the space of a year, while seizures of psychoactive substances has nearly doubled. I would just like a further assurance that the cabinet secretary will be mindful that the successful work does continue and is not compromised in any way. Cabinet secretary, I would like to give the member that reassurance. The reassurance is based on the 17,000 police officers that we have in place and the work that is being done through some new initiatives, psychoactive drugs that are mentioned by the members, and she will be aware of some of the things that have been done in relation to the presence of those drugs in prisons. She will also be aware of recent changes by the Lord Advocate in relation to how those drug offences are prosecuted and dealt with by the police. Yes, there is a real focus on that. Of course, it should not be the case necessarily that the discovery of an increased amount of drugs is necessarily seen as increased prevalence. It may well be due—I am not saying it is—we cannot properly determine exactly what it is due to, but it may well be down to the fact that the police are acting very effectively to locate and seize those drugs as well. To ask the Scottish Government what it is doing to strengthen the process for the handling of complaints and misconduct allegations against police officers. I have partly answered the question in response to Jamie Greene's supplementary question, but, following the review that was mentioned before by Dame Ailey Shangelini, which was into complaints handling investigations and misconduct issues, a number of recommendations have already been implemented. Others, as I have said, will require legislation and will consult on those proposals further to further strengthen the framework for complaints and misconduct allegations against police officers. We will do that next year, including the conduct framework for senior officers. There is, though, currently an established process for the handling of police complaints, investigations of serious incidents and misconduct. I welcome the significant progress that has been made by, among others, the Police Scotland, the SPA, the Police Investigations and Review Commissioner, the Crown Office and the Procurator Fiscal Service to drive improvements in systems and processes in advance of those legislative changes that I mentioned earlier. To ask the Scottish Government what support it is providing NHS Lothian and other NHS boards, given the consequences and impact of delayed discharges. For a very important question, the health and care system is under extreme pressure due to the pandemic, and all health boards are experiencing significant issues, including workforce challenges and high levels of delayed discharge. To help alleviate some of that pressure, we announced a substantial new package of £300 million in hospital and community care to support NHS and social care systems over the winter. A substantial proportion of that funding is going directly into social care to help with delayed discharge. I also announced last month further funding of £10 million to support health boards to maintain resilience throughout winter by putting in place a range of measures, including appropriate levels of staffing at the right place at the right time. I have been meeting with the chief executive of NHS Lothian alongside the chief executive of the city of Edinburgh council and Judith Proctor and the team at the Edinburgh health and social care partnership, as well on a weekly basis for the last month to discuss this very issue. I thank the cabinet secretary for that answer and I'll be very measured in my question because myself and others in the chamber today were at a briefing on Friday, which painted an alarming picture where there has clearly been a spike in delayed discharge, particularly in Edinburgh, leading to a log jam right the way through inpatient care and into accident emergency. Can I ask the cabinet secretary, have in his meetings identified what the issue is? My understanding is that it is not necessarily just one of money. Is this about social care provision or are there other blockages to discharge? Is this an issue that is happening elsewhere in the country? I thank Daniel Johnson. If he wants further briefing, I am happy to speak to him offline with my officials in detail. In terms of the questions that he asks, there are some Edinburgh-specific issues. That is why I meet with Edinburgh every single week because I am concerned about the level of delayed discharge that is the highest in the country, but also the very unique circumstances. For example, there is a severe lack of in-house provision, as he probably knows, not just in care homes, but of course care at home, which is a vital part of keeping people out of hospital, albeit via the back door or preventing them from coming through the front door. Workforce is clearly a challenge in Edinburgh, given that there are other competing workforce pressures in hospitality and so on and so forth. He is absolutely right that finances that I have said to Edinburgh City Council, to the health and social care partnership and to Lothian health board should not be an issue. In fact, I agreed additional funding, recognising that, for example, for interim care placements in Edinburgh, the cost may well be higher in Edinburgh than it would be in other parts of the country. I am convinced and content that funding is not the issues that he articulates, but there are a significant number of other issues that we are trying to work through with Edinburgh. Given the time that I have here in Topicals, I am happy to either write to the member or, if he wants a meeting, I am more than happy to discuss these in greater detail. Indeed, I would welcome more detail and a meeting. A particular concern is in-patient care and particularly within trauma. One particular example is the orthopedics, where delays in treatment can obviously have consequences in terms of bone growth and so on. Is there a particular concern in particular areas of in-patient care and would be able to elaborate that and what action is being taken to remove those issues? Yes, we have concerns right across the board, but he is absolutely right to focus on the areas that he does. What I would say is really important. We can often spend a lot of time in this chamber understandably so focused on unscheduled care, emergency care and elective care. We know that there has been a building backlog due and exacerbated by the significant impact of the pandemic. What we are doing is trying to use all the resources that are possible nationally. For example, we are taking the likes of the Golden Jubilee. How can the Golden Jubilee help with orthopedic surgery, be it in Lothian, be it in the west coast or any other part of the country? We are trying to maximise as much resources that we can to help with the elective backlog. We know that the longer people have to wait for that surgery, the more problems there will be in the future. I am more than happy to go into more details with Daniel Johnson at a meeting. You have announced money for delayed discharges and agreed in your previous answer that money does not necessarily seem to be the problem. When do you expect to help more long-suffering patients to receive the care that they need and deserve by reducing the current level of hospital delayed discharges? As we have reduced in the past week's figures, we have gone below 1,500. It is still far too high, and I want it to reduce even more. I am happy to provide Sandra Scrohani with the latest figures, but I would say that we are beginning to see small levels of reduction, but I need that to be far bigger than it is. I am meeting with the six health boards that have the largest number of delayed discharges and we are working through solutions. We are making some progress, as I said, but I hope that that progress continues. As I have said to Daniel Johnson, I have made it clear to the health boards that funding and finances should not be the barrier to helping to reduce those delayed discharges. I also attended the briefings on Friday with NHS Lothian, and then I went on to one with NHS Borders. Further to the answers to Daniel Johnson, it is not just an Edinburgh problem. Figures for beds as of today at the Borders General Hospital are out of 300 beds. Seven are occupied by Covid patients, but 51 by those whose discharge is delayed. Now, while appreciating the various causes of this, losing 17 per cent of bed capacity with all the predictable challenges this winter lie ahead, we have an immediate problem. Can I listen carefully to the cabinet secretary's answer? If he is also meeting with Ralph Roberts, Ralph Roberts of NHS Borders, it is also a problem in the Borders. You could imagine that I discussed this issue with every single health board. Of course, Christine Grahame is absolutely right. It is a problem that every health board contains with her. There are also areas of very good practice that I am ensuring that is shared right across every single health board. However, Christine Grahame always gets to the crux of the issue here, which is, of course, if we invest, not just in care home placements, which are hugely important, but care at home and making sure that people have the appropriate packages at home, we hopefully prevent them from coming through the front door of the hospital, too. To give her an assurance, I meet with the chief execs and the chairs every single week, of course, Ralph Roberts is on those calls, and we discuss those matters in great detail. I am very grateful for the answers that we have heard today. Following the meeting on Friday, can the cabinet secretary say where the staff are going to come from that are needed to alleviate the problem across Scotland? Recruitment is under way and is going well. DrawBadverse is not just out, but interviews are commencing, and a number of people have already been recruited. I did reference my answer to Daniel Johnson that Edinburgh does have an acute problem, because there are a number of other pressures that are upon them from the retail sector, from hospitality and so on and so forth. However, some of the £300 million of funding that I announced—a bulk or significant proportion of that—was for additional recruitment of band twos to force. That work is very well under way, and I am happy if the member wishes to write to me if he wants more specific detail on recruitment, and I am happy to provide the numbers to him. Stephen Kerr Can I ask the cabinet secretary if he will tell us how many people are now waiting in Scotland for the hospital appointment, given the comments that he has made in relation to capacity in the system? I do not have the figures to hand in terms of exactly how many are waiting for a hospital appointment. I have been happy to look to see if we have those figures and provide them to Stephen Kerr. What I would say is that we are investing heavily to try to free up as much capacity as we possibly can, to get those delayed discharges back out into community, and to help us to free up space within the hospital to see more people, which is important. Of course, our investment in primary care is really important for that, because we do not want everybody to just have to go into hospital to be seen where they can be seen in the community, where they can be seen at primary care, which is why we are making investment right across the entire system. For the exact figures that Mr Kerr is looking for, I am more than happy to see if they can be provided to him.


Hello friends, I am Sanjay Gupta. In this video, I am going to demonstrate you how to use conditional operator question mark in colon in macro in C programming. Before starting, you can note how you can search my YouTube channel. You can type my name Sanjay Gupta in YouTube. My channel will be available there. You can watch various programming related videos here. Now I am going to implement a code in front of you which will demonstrate you how you can use conditional operator in macros in C. So first I am including header file stdio.h. Now I am going to define a macro whose name is Max. It will receive two parameters A and B. And I am implementing this macro with the help of hash defined preprocessor. So now I have to implement its replacement token list. So for that purpose, I am going to use conditional operators. So here you can see this A greater than B is a condition. If this condition is true, then this A will work. Otherwise B will work. So these A and B are placed with the help of question mark and colon. So this complete statement is implementing conditional operator. And this will be replaced wherever I will be using max macro with two parameters. So this is a macro statement which is using conditional operator. Now I am going to define main function where I will be using this macro. So I have declared three integer variables A, B and C. With the help of this print tab, the message enter two numbers will be displayed on output screen. And this scanf will be reading two values from user in A and B variables. Now I am going to use macro whose name is max. So this max A comma B will be replaced with this replacement token list that is A greater than B, question mark A colon B at the time of compilation. So the result will be assigned into C. So I can print the result on output screen with the help of this printf and C variable. So this way I have implemented macro in this program and that macro is using conditional operator. Now I am going to execute this code. It is asking for two numbers. So I am entering 50 as first number and 100 as second number. So you can see the output. It is showing max equals to 100. So it is working properly. So I hope you have understood how we can use conditional operator in macros in C programming. If you want to watch more programming related videos, you can search my name Sanjay Gupta in YouTube. My channel will be there. You can also download my programming app Tagimace which is available on Google Play. Thank you for watching this video.


Russia uses former Wagner mercenaries as cannon fodder near Skadovskaya. The Russian Federation has reportedly relocated former fighters from the Wagner private military company to the temporarily occupied Skadovskaya according to the National Resistance Center of Ukraine. According to the center near the temporarily occupied Skadovskaya in the Kursan region, the Russians have set up a camp where former fighters of the Wagner group are located. According to underground sources, the former Wagner militants are now provided with anything. The logistical problems are entirely shifted onto so-called volunteers. Former mercenaries lack transportation and personal protection equipment. Currently, the command of the Russian occupation forces on site is determining the further deployment of these fighters. According to British intelligence, hundreds of fighters formerly associated with the Wagner group have started redeploying to Ukraine individually and in small groups to participate in the war as part of various Russian units. As stated, Mykhailo Podoliak, an advisor to the head of the office of the president, these remnants are filing gaps in the Bakhmut direction and the Wagner group itself no longer exists. Ilya Yevlash, the spokesperson for the Eastern Operational Command of the Ukrainian Armed Forces, reported that Wagner group mercenaries are present in the territory of the Eastern Operational Command. Currently, some of the mercenaries are negotiating contracts with the Russian military and returning to Ukraine from Belarus.


So, I will be talking about some other discrete probability distributions. So, the next one is the negative binomial random wearable and this is the name is very suggestive. We took the, we considered the binomial distribution, which where the random wearable was representing the number of successes, where the number of trials is fixed. So, you had, you have to perform in trials, probability of success is p and then we asked for the probability of r successes. Now, here it is the reverse, what we are saying is that independent trials are performed, probability of success is p, p between 0 and 1, trials are conducted till r successes occur. So, now it is the opposite, that means now you go on conducting the trials till r successes have occurred. And so, x will be the number of trials required for r successes. In the binomial case, the trials were fixed and you had to then ask for the probability of r successes. Here the number of successes is fixed and you are saying what are the number of trials that you required. So, that r successes take place. So, therefore, if you now take, so here the random wearable is the number of trials. So, probability x equal to n and it is very simple to write it down, because so that means see you will stop your experiment the moment you hit the rth success. So, that means up to n minus 1 trials, if I want r successes to occur in n trials, then up to n minus 1 trials r minus 1 successes should have occurred.  So, therefore, the total number of successes add up to r, but you are here wanting r minus 1 successes to occur anywhere up to the up to n minus 1th trial the last trial must be. So, the nth trial in this case must be a success and so your n can vary from r r because you want r successes. So, at least r trials have to be conducted.  Now, since the experiment continues till r successes occur. So, therefore, when you add up n equal to r to infinity probability x equal to n, this must add up to 1. And therefore, this is a combinatorial argument to say that what we have defined here is a probability mass function analytically also one can show that this sum will equal 1, but then you require little more mathematics. So, therefore, we just satisfy ourselves by giving this combinatorial argument that they will continue this trial still a success occur the rth success occurs. And also probability x equal to n is non negative for n varying from r r plus 1 and so on. So, this defines a PMF. So, this is a valid PMF when r is equal to 1. That means, if you are just looking for the first success then x is the number of trials required for the first success then obviously, you put r equal to 1. So, that becomes 1 and so this is 1 minus p and minus 1 into p. That means, the first n minus 1 trials must end up in failure.  So, 1 minus p raise to n minus 1 into p and n can vary from 1 onwards. X is now called the geometric random variable and the corresponding PMF is the geometric distribution. Now, interesting application of a negative binomial random variable and the distribution. So, this is known as the Banach match problem. Banach was a very famous mathematician and he was a heavy pipe smoker. So, that he does not waste time in looking for the match box and then lighting up a match to light his pipe. He would carry two match boxes, one in his left hand pocket and the other one in the right. So, that wherever he puts his hand he gets a matchbox and then he lights his pipe. So, therefore, that is how he was dependent on smoking his pipe. So, each time he needed a match he would equally likely take it from either of his pockets. It should be either of his pockets. So, it was equally likely that he would put his hand in the right hand pocket or on the left hand pocket. So, probability of that is the same. And now, consider the moment when the mathematician first discovers that one of his matches is matchbox is empty. So, now, assume that both matches initially carried both match boxes I should say. So, both the match boxes initially carried capital N matches. So, we are asking what is the probability that the other match box contains exactly K matches. So, that means initially both had capital N number of matchsticks in the match boxes and then when he discovers that one of the match boxes is empty, then the other one contains exactly K matches. So, this is what we have to find out the probability of this event now. So, let us say that consider the case when the left hand pocket has K matches left. So, that means the right hand pocket is empty and the left hand pocket has the match box has K matches left. Here again I should say when the left hand pocket match box is having K matches left. So, I have left out the match box. Thus the mathematician discovers the empty pocket at the, see he emptied the N match sticks in the right hand pocket and here he emptied N minus K because K are left in the left hand pocket and then on the N plus 1 th when you put his hand in the N plus 1 th or when he takes out the match box at the N plus 1 th time I mean from the right hand pocket then he discovers it is empty. So, the total number of trials are N plus N minus K plus 1. So, exactly the situation of a negative. So, taking out a match stick from the right hand pocket as a success. So, we will take taking out as a success, we will treat it as a success. So, let us say that. So, we will say that the right hand pocket taking out or putting the hand in your right hand pocket and of course, when you put as long as the match box has a stick you are also taking out a stick match stick. So, therefore, whichever way you want to put it, but anyway taking out a match stick from the right hand pocket is a success. We are looking for the N plus 1 th success, but where actually he discovers that it is empty. So, that is a consequence of the match box getting emptied, but essentially what we are saying is that putting his hand in the right hand pocket is a success and putting his hand in the left hand pocket is a failure. So, random variable X which is equal to the number of trials required for N plus 1 successes. So, this is exactly the case for a negative binomial distribution and what we are saying here is that this is actually that means this is happening when you have had this many trials N plus 1 plus N minus k. And therefore, by our argument see the last one he discovers that it is that means at the 2 N minus k plus 1 th trial he discovers that the left right hand pocket does not match box does not have a any sticks left in it.  So, this will be the probability that, but then since either of the pockets could have emptied first. So, therefore, what we are saying is twice this. So, the required probability is since either pocket can be emptied required probability is twice of that and so when you multiply by 2 this 1 disappears and the required probability is 2 N minus k choose N into 1 by 2 raise to 2 N minus k. Now, again these results I am just giving you without because handling this thing requires lot of mathematics you will not do it. So, I will just simply say that expected value of a random negative random variable which has parameters r and p that means r number of successes are required and p is the probability of success that is r by p and the variance of a negative binomial r comma p random variable is r into 1 minus p upon p square. So, for example, if you are throwing of a dice x is the random variable which is the equal to the number of throws of a die required till number 1 shows 5 times.  So, probability of each number showing up is 1 by 6. So, probability of number 1 showing up is 1 by 6. So, our p is 1 by 6 r is 5 and therefore, by this these two formulae expected value of x is 5 upon 1 by 6 which is 30 and various that means at least the expected value that expected number of trials required to require throws of the die required. So, that number 1 shows 5 times is 30 and the variance is again by this formula comes out to be 130 or 25 into 6 no that is 150. So, this is 150. So, that is about negative binomial and geometric distribution. So, another discrete random variable which is quite useful is hyper geometric random variable. So, I will demonstrate this through an example or define this variable and the corresponding distribution.   So, I keep taking out the balls and put them aside fine. So, now, if x is the random variable which counts the number of white balls selected.  So, k can obviously vary from 0 1 to m because there are m white balls. So, the probability would be now here you see we are using the multinomial distribution.    Now, here of course, this is meaning when k is such that n minus k is less than or equal to n minus m because see there is some connection between m k and n. So, obviously, I cannot if my number m is very large then I can select k number of balls, but then n minus k becomes negative or n minus k is. So, that means it has to be less than or equal to n minus m, but then see by convention if n minus k turns out to be greater than n minus m or n minus k is less than 0, but the convention we say that this n minus m choose n minus k is 0. So, therefore, this has a meaning. So, we do not have to worry because then there will be the probability would be if k is such that n minus k is greater than n minus m or n minus k is less than 0 then these probabilities will be 0 and so there will be no mass attached with that those values of k.  So, this takes care of all possible cases and therefore, this is a this is a genuine this is a valid PMF. So, that means what we are saying is that summation probability x equal to k, k varying from 0 to m is equal to 1 and also these probabilities are all non negative. So, therefore, this is a valid PMF. So, that this exercise we must do every time we define a random variable and it is corresponding probability mass function. Now, let me just show you an example of where we use where we make use of hypergeometry random variable and it is a distribution except in sampling in quality control. So, what you do is of course, I will give the numbers here are small, but usually the numbers are much bigger than what I am using here. So, suppose 200 items in the lot some some instrument or something is being delivered by a manufacturer the whole lot is of size 200 and the claim by the manufacturer is that no more than 10 percent are defective. So, this is the claim. Now, obviously, people do not have time and energy and manpower to actually inspect all the 200 items and usually this number is very big. So, what did what the practice is and that is why it is acceptance sampling. So, what you do is after the shipment is received a sample of size 10 is taken again the numbers are all just for convenience sake, but usually there will be more realistic numbers. So, anyway a sample of size 10 is taken without replacement and if there are at most too defective the lot is accepted. So, you just at random choose a sample of size 10 from this whole lot of 200 items and then you inspect those 10 items and you have taken out the sample via without replacement. So, you inspect those and then in that sample of size 10 if you find 0 1 or 2 defective you will accept the whole lot and you will say that it is and if there are more than 2 defective then you will reject the lot. So, this is what you call acceptance sampling in quality control.  So, that means for example, if 5 percent are defective in the entire lot then it carry it contains 10 defective and 190 non defective. So, here the claim by the manufacturer is that no more than 10 percent are defective. So, let me consider the case when 5 percent are defective in the entire lot then it contains 10 defective and 1 because 5 percent of 200 is 10. So, 10 are defective and 190 are non defective. So, now if you want to compute the number of defectives in a sample of size 10 x is rather this then you want to compute the probability that x is less than or equal to 2 which means probability x equal to 0 plus probability x equal to 1 plus probability x equal to 2. So, this is what you want to compute and see I will just show you the calculations here. So, what I am showing you here the probability of number of defectives being small x. So, that will be this is the case when we are say assuming that 5 percent are defective in the whole lot. So, then it is 10 choose x and then 190 are non defective from the non defective I am choosing 10 minus x and then divided by 200 choose 10. So, this is the hyper geometric probability of choosing x defective or the sample size is containing x defective our sample size is 10. Hence, probability of accepting a shipment that has 5 percent defective. So, we are saying at most 2 are defective in the sample size of 10. So, that probability would be probability x equal to 0 x equal to 1 and x equal to 2 which I have written down here and if you look at the numbers these are the 3 probabilities you add them up and they come out to be 0.990935 that means the probability of accepting the whole lot is 0.99. Now, if there are 10 percent defective then there are 20 defective in the whole lot and 180 non defective. So, in that case the hyper geometric probability of x defective in your sample of size 10 would be 20 x and 20 choose x 180 choose 10 minus x because you are taking a sample of size 10 and divided by 200 choose 10. So, this will be the probability of having x defective in your sample of size 10 which is taken without replacement. So, therefore, in that case the probability of accepting the shipment that is 10 percent defective again we want the number of defective in the sample to be not more than 2. So, it can be 0 1 and 2. So, these are the numbers and here the probability is 0.9347. So, this is less than the probability that we attained for when the shipment had 5 percent defective. That is the probability of accepting a 10 percent defective shipment is smaller than the probability of accepting a 5 percent defective shipment. So, of course, obviously the less the defective the more the chance of accepting the shipment because the probability of getting 2 at most 2 defective in a sample of size 10 will be smaller if 5 percent are defective and when 10 percent are defective this is what it is saying. And therefore, you can experiment with other values of the number of defective items in the whole lot and then you can compute the probabilities accordingly. So, relationships among hyper geometric binomial and Poisson distributions. So, let me show you I have already shown you how binomial will approximate to Poisson when n is large and the number of trials is large and your n p converges to a moderately small number. So, now here let me show you the interconnection between all these 3. In fact, 4 discrete random variables that we have discussed so far. So, now again we say that population is of n objects and number of a number of a number of type a objects are there in the population. So, the others are not a type and a sample of size n is drawn without replacement small n. So, a sample of a size small n is drawn without replacement where of course, n has to small n has to be between 1 and capital n and a has to be between 0 and n. And while discussing the hyper geometric series I told you that even if this number is bigger than this then by convention this is 0 and so there will be no mass. So, we really do not have to worry about the values of as to what the when I am writing this oh sorry this is x. So, now if I want to n let p be a by n this is the proportion of item I am not using it now I will be using it later on. Anyway this is the proportion of items item of type a of type a in the original population. So, I am denoting this by p which I will make use of later on. Now, this probability that is your sample size of small n contains x objects of type capital A. So, that will be choosing from small a x right. A is the total number of type a objects you want to select. So, your sample should have x of them. So, this is a choose x then remaining the population n minus a are the other kind of objects from this you are choosing n minus x other kind of objects divided by the total ways in which you can choose a sample of size small n from capital N. Now, just write out these expressions. So, this will be a factorial divided by x factorial a minus x factorial this will be n minus a factorial divided by n minus x factorial n minus a minus n plus x factorial. And then this is the denominator. So, this flips over and you get here in the numerator n factorial n minus n factorial divided by n factorial. So, let us simplify this expression what I will do is this n factorial comes here then x factorial and n minus x factorial this I put together and you can see that I am heading towards the binomial distribution. And then you see here a factorial divided by a minus x factorial. So, the terms after a minus x plus 1 will cancel out. So, you will be left with a a minus 1 a minus x plus 1 from here and this is gone. Then similarly, here this many terms will go away. So, you will be left with n minus a n minus a minus 1 up to n minus a minus n plus x plus 1. One more from here that will be up to that many terms. And then here similarly, n factorial I have used here now here n minus n factorial. So, those terms will cancel out and you will be left with n n minus 1 up to n minus n plus 1. So, this is from here to here this is fine. Now what I am doing is yeah. So, this term this I can write as n choose x then from here if I remove a from each of this then this is a raise to x because this is a a minus 1 a minus x plus 1. So, x minus 1 a is come from here and this is the x at a. So, a raise to x this comes out then similarly, if you remove n minus a from here from each of them from each of these terms n minus a. So, that will also be in number n minus x because this is n minus x plus 1. So, when you include this one you will get this. So, this is a 1 and then this is this. So, similarly here it was it would be 1. So, 1 minus 1 upon n minus a and this is what you have and then n raise to n we have taken because here this is minus n plus 1. So, you take out n from each of them and divide correspondingly. So, you will have capital n raise to small n that is this here. Now what I will do is yeah I should have written down this step here what I am doing is I will write this as this is this. So, I will write this as maybe I will do it here. So, this is n c x then a by n raise to x out of this and then into divide by n. So, 1 minus a by n raise to n minus x. So, all this is equal to this which is your binomial probability of choosing x items from n and that means your number of defective or number of type a items from the sample size n is this probability is that and now this you see here what we are saying is that x by a is small that means a is a big number large number that means the number of type a objects in your total population is large. Then this number is also small and this number is also small that means your capital n is very large in such a situation you can see that all these numbers go to 1 all of them and this also goes to 1. So, this whole reduces to approximately number 1 and so this probability hyper geometric probability of choosing a particular type of objects in your sample that probability reduces to the binomial. Now I should have did not probably pointed out here see when we conduct the binomial experiment we say that the trials are occurring independently and then you keep counting the number of successes. So, in other words in this situation the binomial experiment would be when you are replacing the balls right because getting a white ball is a success and. So, in the binomial situation you replace back the ball that you have taken out. So, each time the probability remains the same of getting a white ball which is equal to a by n right see here a by n p. So, this actually comes out to be this p raise to x 1 minus p raise to n minus x. So, this is what I wrote right. So, therefore that means the difference between a hyper geometric and binomial is that you know for small values of the population size it is without replacement the hyper geometric right. But if you make the population size large and as I said all these three numbers should be small in that case the hyper geometric reduces to approximate is approximated by the binomial probability right. And I have already shown you that binomial can be approximated by Poisson where we were saying the same thing that yes that this should be small right. So, in this case n into p our p is our p is a by capital N. So, this number should be moderately small then we say that for capital N being large then we say that the binomial can be approximated by Poisson or the binomial probability goes to Poisson. And here I have shown you that a hyper geometric goes to binomial and by the same argument that I have shown you here when I talk about and I take lambda to be N into A by N then you can show by again manipulating the terms that the hyper geometric will go to Poisson. And I already in the earlier lecture I have shown you that Bernoulli is binomial 1 p right. And so the relationship is there that when you and you have N when you add up N Bernoulli random variables you get the binomial. And so this diagram shows you the relationship between the various discrete distributions that we have discussed so far. . So, let us now look at the other type of random variables which are continuous random variables. So, far we have looked at discrete random variables and their special cases. Now, I will want to describe continuous random variables and then again we will look at the special cases of continuous random variables. So, essentially these are random variables for which possible outcomes for which a possible outcomes are uncountably infinite. So, here you cannot count and therefore, for example if you take a subset in R 2 then the number of points is uncountable. And similarly if you take an interval on the real line and you consider all possible real numbers then that is a uncountable set. Examples are lifetime of a transistor. So, of course, you do not know when exactly a transistor will fail, but and see you might say that because you have finite clock. So, you can say that it failed at this but that means you can actually say that the lifetime is finite, but then it depends on your counting system. I mean if you as fine as you find as you make it then you know the lifetime you can treat this as a uncountably infinite. The arrival of a train at a station and so on. So, one can go on adding list to this and as we go through the as we go through the this topic we will come across so many continuous random variables. Now, one way to define a continuous random variable would be that suppose there is a non negative function f x defined for all real x and on the real line minus infinity to infinity having the property that for any set b of real numbers the probability that x belongs to b is integral of the function this non negative function f by d y over b and so here by our definition we are saying that if x belongs to the whole real line then the probability of that will be integral minus infinity to infinity and f by d y is 1. So, we are putting this condition and therefore, by definition f is a and so f is now known as the probability density function as opposed to probability mass function because now this is the continuous case. So, we differentiate between the continuous and discrete by. So, in this case the function is probability density function and for the discrete case we called it probability mass function. So, this is the for the for the random variable x. So, therefore, x is therefore, if there is a function like this and if it satisfies these conditions. So, it is a non negative function when we say that f is the probability density function of the continuous random variable x. So, let me give you some more idea about continuous random variable. So, you know one can also define a random variable x as a variable whose distribution function is continuous everywhere. So, actually the name continuous random variable has come from here because the distribution function of a continuous random variable is continuous that is why we call the random variable continuous. So, actually it is not that there is nothing about you know calling a random variable continuous or discrete. We actually say random variable is discrete because it is a cumulative distribution function is discrete that means it has jumps and we say that a random variable is continuous if its distribution function is f x is continuous. So, this is everywhere that is one definition. The another one can be a random variable x is said to be absolutely continuous if there exists an integrable function f x from r to r such that f x is non negative for all x belonging to r and its distribution function f x satisfies the equation that f x of x is equal to minus infinity to x integral of f x t d t x belonging to r for any real number. That means the probability x less than or equal to small x that probability is obtained as integral of minus infinity to x f x t d t x belonging to r. So, and then if you see that since the distribution function has the property that limit f x x as x goes to plus infinity is 1. So, therefore you see the value of this integral minus infinity to infinity f x t d t will also be equal to 1 and hence the function small f x that we are saying has to be non negative is actually the p d f for the for the function x.  Anyway, so the thing is that most of the time in this course I will not be saying absolutely continuous of the time, but whatever is absolutely continuous I will call it continuous and then I will distinguish between a mixed random variable. So, that means a discrete random variable, mixed random variable and continuous random variable. So, what I refer to as continuous random variable will be absolute is actually by definition absolutely continuous, because the way we have been handling we are defining the continuous random variables and the p d f in this course the definition this definition is the right one. I mean we are following this definition that capital F x x is equal to minus infinity to x f x t d t x belonging to R. So, whichever way, but I just thought that one needs to say a little more than what I had said in the lecture about a continuous random variable and of course, through examples we will come to know quite a bit more about the various kinds of continuous random variables that we come across and their properties. Now, if b is an interval then a probability x belonging to a comma b will be a to b f x d x and that is what I am trying to show you that if this is the curve of f x then this implies that it is actually the area under the curve and of course, I have written it out here that in terms of your I will come to that. So, then and if a is equal to b then this reduces to probability x equal to a and that means a to so this sorry b a. So, the integral will be from a to a f x d x and by again definition of the integral this is 0. So, therefore, mass at a point for a continuous random variable is 0 that all the probability that a continuous random variable assumes a fixed value is 0 this is what we are saying by this right. And therefore, so I will come to this point is that see the interval I have been writing as an open interval, but here I have written as closed. So, it does not matter because whether you include the point a or the point b or both the masses at the individual points at the fixed points a and b are 0 that means no probability attached to fixed values of the random continuous random variable. Therefore, it does not matter whether I write it as this or as I write it as an open interval. And then so since the probability x less than or equal to x I am sorry this is not correct I want to say here this is x capital X. So, this is now we are defining the cumulative distribution function or the probability that x is less than or equal to x and this will be in by our definition minus infinity to x of f y d y. So, this is the cumulative distribution function of x and from the figure we can see that this is again f b minus f a. So, that means this will be the area from minus infinity to a under the function f x that is f a and then this area up to b would be f b. So, you are essentially looking for the area between the in the strip and inside this strip and so this is area under the curve. So, we have I have shown you that for the x is a continuous random variable then the cumulative distribution function has been defined according to this and so we can also then I have the concept of the probability in an interval a to b and that is area under the curve. Now, let me just make two particular I mean emphasize two points here that you see as opposed to a discrete random variable where it was important whether in an interval when you are talking of probability of random variable in an interval then whether the end points are included in the interval or not for a discrete random variable it mattered because every point has some positive probability I mean or non negative. Now, for a continuous random variable you see it does not really matter because there is no concept of a probability at a point that concept is the idea that at a point the probability is 0. So, therefore, whether I say a less than or equal to x less than or equal to b or a strictly less than x less than or equal to b has no relevance. So, therefore, it is understood and see that is why I am writing the integral from a to b here f y d y. So, for continuous random variable at a point there is no concept of probability or the mass whatever or the density because it is a density. So, we measure it on an interval fine. So, and secondly for a continuous random variable we will call it cumulative distribution function that is the proper notation. And here again if some places it may just happen that without realizing it I may have used the word density, but does not matter the idea the proper notation is that it should be cumulative distribution function when your random variable x or in fact for this notation holds for x continuous or discrete random variable. So, the word is cumulative distribution function we saw that for a discrete random variable it was a summation and here it will be in the form of an integral because you are computing the probability of a continuous random variable over an interval. Now, we want to check that f x has the properties of a c d f and so the first thing you want to check is that this limit of f x x as x goes to minus infinity will be 0. So, I should have said that this is equal to 0 here and of course this is immediate because limit as x goes to plus infinity would be this integral minus infinity to infinity f y d y and since f is a probability density function by definition minus infinity to infinity this integral should be equal to 1. So, that part is now for this again the argument may look repetitive we have already used it elsewhere, but let me just repeat it. So, let x n be a decreasing sequence such that x n is going to minus infinity. Now, we define the events e n which are all points in the sample space for which capital X is less than or equal to x n. Then you see again e n this as n goes to 1 to infinity is a decreasing sequence of events and limit e n as n goes to infinity will be empty because you know as n goes to infinity you will be talking of event where x is less than or equal to minus infinity. So, there can be no real number which is less than minus infinity and therefore, limit e n goes to infinity is phi is the empty set and again by continuity of the probability function you will say that probability of limit probability e n as n goes to infinity is same as limit probability e n as n goes to infinity by continuity and therefore, this will be phi because the probability of a empty set is 0. So, this property is also satisfied and we will verify the other properties also. .. And for to show that it is monotonic for a less than b this is f x we want to show that f x is less than or equal to f b.  Now, this is non-negative f is a non-negative function this is a finite interval because b is greater than a. So, again this number is something non-negative therefore, your probability or your f x b is bigger than f x a. And so the function capital f is monotonic and therefore, it satisfies all the conditions for cumulative density function and hence we have a proper definition is a proper here. Now, the question if you just define a function like this and you ask whether is it a c d f of random variable x then what do we all need to verify we need to verify that for minus infinity. So, that means you need to verify that minus infinity to 0 e raise to x by 2 d x this is equal to what see it should for minus infinity to infinity it should be 1 this should sorry I am showing that this is a c d f. So, this is not p d I mean I am not checking it is p d f. So, what is happening is e raise to x by 2 limit as x goes to minus infinity because this is x less than 0. So, as x goes to minus infinity this should go to 0. So, that is fine because x goes to minus infinity e raise to x will go to 0. So, this goes to 0. Now, look at limit 1 minus e raise to x by 2 as x goes to plus infinity. So, what is happening here this because this portion goes to infinity. So, therefore, this is going to minus infinity and not equal to 0. So, therefore, this does not define a c d f and. So, we can continue I mean one can try to see if any one of the condition fails to be satisfied here we will conclude that the function that we are looking at is not a c d f and similarly as we have done it for the discrete get also we check verify when we define a continuous random variable that the whether it is a valid p d f or not probability density function. Then I will also try to later on give you examples where the random variable can be the mixed kind. That means, some for some portion of the real line it may be discrete it may behave like a discrete random variable and then for some points on the real some portion of the real line it may be a continuous random variable. Now, another thing that I want to point out is that since you are defining your c d f as this. So, necessarily by the theory of integral calculus it turns out that this has to be a continuous function. So, that is another way of differentiating between that means for if for a certain part of the real line your c d f is continuous then we will assume that the corresponding the part of the random variable is a continuous random variable right and we saw that when it is a discrete random variable your graph of capital the c d f has jumps and the jumps are equal to the probability of the random variable at that particular point. So, definitely. So, therefore that means you can have now c d f which is for in part step function and in part it is a continuous function. So, I will try to give you examples of such and then that case we will say that the random variable is the mixed kind. So, that means all kinds of random variables exist discrete mixed kind and continuous. .


When the world's on fire, don't you want God's voice for to be up below? Hide me over in the rock of ages. Rock of ages, clap for to be up. To listen to your word, then bless us with the Son of God. A peace, Sabbath, to you boys and girls at home and here in church. Last Sabbath, we were taken through a very, very interesting journey of Paul, moving all the way from one island to another. And finally, ending up in Jerusalem. And while in Jerusalem, he was apprehended and met the very rowdy group of people. But before we continue with today's book that is Acts chapter 22, I would like to introduce the guests who are here with us this morning. And to my far right is Mike Momane, Tamara Mora, Tessie Bahati. We are the great three learners at Maxwell Adventist Preparatory School. Well said, and my name is Teacher Mary. Welcome once again. Today's theme is Gospel in Chains. Well done, Gospel in Chains. So while Paul was in Jerusalem apprehended, he was taken all the way up to the forts from one step to another. And Paul decided to take heed to the orders of the commander. When he was a few steps away, Paul turned back and looked at the commander and requested to make a defense against his accusations. Tamara? Yes? Suppose you were Paul. What sort of defense would you make? Indeed, a Jew born in Tassas in Sicilia, but brought up in the city at the feet of Gamalien, taught according to the strictness of our father's laws and resilience to God as you are all are today. Well said, Tamara. Very good indeed. We have had Paul's spokes using certain language, Tessie, what sort of language do you think Paul used? Paul used Hebrew language. Well done, and why do you think Paul used Hebrew language? Paul used Hebrew language so that the people can know he's one of them. Very good. It was very important for Paul to have used Hebrew language so that the people there would know that indeed he was one of their kind. Hmm, Mike? Yes? There was a name mentioned there. What name was that? Gamaliel. Gamaliel, very well. And who was Gamaliel? Gamaliel was a respected man of the law, and he was the teacher of Paul. Very good. Therefore, it was very important also for Paul to have mentioned the name Gamaliel, because he was very acquainted with one, the Mosaic law, and two, the customs of the Jewish people. Well done, and well done indeed. Ma, would you tell us the next defense that Paul made? I persecuted to death the people who followed this way. I arrested men and women and threw them into prison. The high priest and the council can prove that I'm telling the truth. I received letters from them to fellow Jews in Damascus, so I went there and arrested those people and brought them back in chains to Jerusalem to be punished. Ah, well done. Sit down. Good boy. Isn't it so sad to note that Paul arrested people and then took them all the way to Jerusalem to be punished? Oh, it's indeed very, very sad. Tessie. Yes? How are you? Fine. Good, Tessie. So would you like to tell us more of the defense that Paul made? As I was traveling coming here, Damascus about midday, a bright light flashed from the sky. I heard a voice saying to me, soul, soul. Why do you persecute me? The people with soul did not hear the one who was speaking to soul, but saw the bright light. What shall I do? Get up and go to Damascus. Why you will find the Lord as the charming for you? I was blind because of the bright light. So my companions took me by the hand and led me to Damascus. In that city was a man named Ananias who was respected by all the Jews living there. He came to me and said, brother soul, see again. At that very moment, I saw again. I looked at him and he said, the Lord of our ancestors has chosen you to do his will, and you will be a witness to everyone who has heard and seen. Why wait any longer? Get up and be baptized. And at that moment, I went to the temple to pray back in Jerusalem. And as I was praying, I saw a vision. And in that vision, Christ was telling me to quickly move out of Jerusalem because people there were not going to hear what I was saying. And before Paul could finish, the mob started chanting and screaming, crucify him. Crucify him. Crucify him. He is not fit to live. He is not fit to live. And the soldiers kept on pressing so hard against Paul and pushing him farther and farther to the fort. And at that point in time, again, Paul turned and looked at the soldier who was there and requested to make just the last point. Tessie, do you think he's saved? He's saved. Is it right for you to whip a Roman citizen? Well done. Was Paul persecuted?  Was he thrown in a dungeon? Well, boys and girls, be sure to join us next Sabbath as we shall be looking at the book of Acts chapter 23. But for now, it's bye.


Okay, so let's do this particular redox equation. It says, consider the reaction iron plus copper 2 goes to copper plus iron 2. Which statement is true for the reaction? And then it gives you these statements and it wants you to identify which one. So, a copper 2 plus is oxidized, b iron increases in oxidation state, c copper 2 plus is reduced, d iron is reduced, and e 2 of these choices are correct. Okay, so the first thing I want you guys to remember is that when you lose electrons you're oxidized, okay, and when you gain electrons you're reduced. Okay, so that should help you to look at some of these choices and tell well what's going on. So, the first one talks about copper 2 plus. Let's just not worry about what it says, but let's look at what's going on here. So, it's going from the oxidation state here is what? 2 plus. What's the oxidation state here? Zero. So, it'll go from 2 plus to zero must have done what? Gained electrons. Yeah, gained electrons, okay? Or got reduced. Yeah, okay. So, did it get oxidized if it got reduced? No. So, that one's definitely not correct. Okay, so did it get reduced? Yes. Yes, so that one is correct. Are we okay with that? Yeah. That's it? Okay. So, now let's look at this one. What's the oxidation state here? Zero. Zero. And what's the oxidation state here? 2 plus. Okay, so to increase in oxidation state that means to go from a smaller number to a bigger number, right? So, did that happen with iron? Did it go from a smaller number to a bigger number? Yes. Yes. So, that is correct as well. Okay. So, did it get reduced? Iron get reduced? No. No, it didn't get reduced, right? It got oxidized. Okay. So, cancel that one. Okay. So, what is the correct answer? Well, since B and C are both correct, right? Two of these choices are correct. Any questions on this one? No. Okay. Pretty straight.


So it's pie day. Gotta make a pie. And there's two parts to making a pie. The crust and the filling. Say a blackberry filling and a butter crust. Sugar goes in the filling, salt goes in the crust, but there's flour in both the filling and the crust, so that's convenient. We only have to add it once. Then grab your ven spoons and mix it up. Yeah, that's looking pretty good. And here's our finished crust. And since we're tau fans here, let's make two pies. That intersect. Okay, in goes a blackberry filling. In, in, in. But what filling for our other pie? Let's use fresh peaches. Chop, chop, chop. Okay, there we go. So we have a blackberry peach ven piagram, but what goes in the middle? You might think a mix of the two for a blackberry peach pie, if you're thinking of each pie section as an entire category. But if you're thinking of each individual thing in each section, it wouldn't make sense to put peaches in the blackberry circle or blackberries in the peach circle. And there's no fruit that's both a blackberry and a peach yet. But maybe you could put plums in the middle and have the categories be stone fruit for peaches and plums, but not blackberries. And then both plums and blackberries, but not peaches, are in the category of fruit that you can eat without feeling weird about biting something so soft and cuddly. Then you could put apricots in with the peaches, nectarines in with the plums, and lots of stuff in with the blackberries, if you wanted. But I don't have all that, and we need something for this middle section. And the obvious answer is fish. Fish makes sense. Because the pointy ovally shape of the middle section, if the circles are overlapping so it's that they intersect each other's centers, this shape is called vesica pisces. Pisces like fish, and vesica means bladder. Fish bladder. That's what this shape is called, so I put fish in it. Well, people put fish on pizza, and that's a kind of pie. Okay, so it's pie day, gotta make a fish pizza pie. Pie has two parts, the base and the toppings, and the dough is the base, and the tomato sauce is somewhere between a base and a topping. I mean, I'm from New York, so I have opinions, but sure, now that I'm on the west coast, I can accommodate people who think even cheese is optional by thinking Venn diagrammatically about my pizza, instead of just having black and white opinions about everything. And in the last section goes things that are just topping and not standard pizza base, like anchovies. Okay, so we're going to have two overlapping pies, one for saltwater fish and one for freshwater fish. Anchovies are saltwater, so are mackerel, and then some freshwater trout, and you know what's a freshwater fish and a saltwater fish? Salmon! All that work to swim out to sea and then jump back at waterfalls to spawn just so they can end up in the honorable Vesica Pisces position of the pie day Pisces pizza pie diagram. Okay, let's get that in the oven, but how are we going to cut it once it's done? Luckily Euclid figured this one out thousands of years ago, just pretend you're doing a ruler and compass construction of the equilateral triangle. Draw a line through the two circle centers, then lines from the centers to the circle intersections. And if you actually wanted to use a number pie today, here's some homework, and it actually smells really good. Let's check it out. Oh, perfect. There we go. A pie day Pisces pizza pie diagram. Okay, happy pie day. Bye. Oh wait, let's do Euclid to it. Okay, yep, we sure did some geometry to a pie with fish on it. Okay, bye.