Good afternoon, everyone. Yes, I'm one of the practitioners of CICD at MyData. I just introduced myself. I'm Oma Mukhera, CBO co-founder of MyData. I actually applied for a talk to talk at this conference about CICD. Then Priyanka said, why don't you actually moderate this panel? Because there are a lot of experts which you could ask some good questions on. So happy to be here. Why don't we all introduce ourselves before we get started. Hi there. My name is Anna Medino. I currently work at Gremlin as a chaos engineer. We help companies build more resilient systems by proactively injecting failure. Prior to this, I've worked on cloud infrastructure at Uber as well as chaos engineering there. And I've been working in software engineering for about 10 years now. Hi, everyone. My name is Angel Rivera. I'm a developer advocate at Circle CI. And at Circle, we enable developers to build tests and deploy their software at scale. Yeah, I started with Circle about a year and a half ago, a little over a year and a half ago. And I basically come to conventions, conferences, meetups, whatever, and do grassroots engagements with individuals and teams on how they're using technology. Hey, everyone. My name's Dan Ver. And I'm a co-founder and lead on the CNCF.CI project. And what that project aims to do is test CNCF CI projects and does interoperability testing. So we want to test things like what versions of Kubernetes do these projects work on and to make sure everything's compliant and then do matrix testing out. Does this version of QoDNS work with the stable version of Kubernetes and so forth? And my name is William Chia. I am part of the product team at GitLab. I work most with CI CD and Ops, which means I get to work with Kubernetes and our serverless features in GitLab. And I work specifically on the go-to-market side of our product team, where I get to work mostly with customers hearing from everyone from startups and small businesses to large enterprises what they're doing every single day in regards to CI CD, Kubernetes, and multi-cloud. And I took a photo of you all because you look great and it's on Twitter. Hey, my name is Frank Ford and I am an IT architect at Genworth, primarily working with helping enable our internal development teams to build CI CD solutions. Great. The previous panel was also interesting. I picked up two things just to recap. Kubernetes made the multi-cloud journey easier and faster, but I think it was Wix who said from Google, Kubernetes doesn't solve CI and DevOps problem. That's an interesting one. So while I think we have real users here, practitioners on CI CD and of course, we're going to find out they do use multi-cloud in their daily practice and how they actually using CI CD. So why don't we generally go around the panel and say, do you use any cloud provider in your daily lives and other multi-cloud involved already? So Gremlin actually is only using one cloud provider. We're strictly on AWS. But I get to work on the developer advocacy team. That's kind of like the community side of Gremlin. So we actually play around with all cloud providers. I mostly stick to using Azure, AWS, Digital Ocean, and Google. So most of my experience is actually playing around with Kubernetes and building out environments that sometimes we play around with CI CD or actually implement multi-cloud technologies around it. But for the most part, like as a company, we still haven't gotten to the point of going multi-cloud. But I actually did get to experience trying to move Uber to go multi-cloud. I was part of the cloud infrastructure team there where we were assessing being completely bare metal and trying to move to the cloud. But we wanted to do that in a very non-vendor agnostic way. So we're actually implementing the API with AWS and GCP and trying to build out a way. And from what I recently heard, they now have a tripod model implemented into Uber that they're still touching two clouds and keeping their bare metals at data centers. Yeah, so at Circle, we're definitely doing multi-cloud. Presents a lot of challenges. We have to run your code, right? And we have to have the ability to provide the functionality from the different cloud providers, specifically Mac, right? That's a really hard one to solve. That one, we actually have our own private cloud that we built out, right? Because of the restrictions in the Apple ecosystem. But we also added Windows recently. So that's presented a challenge for us to adapt to Azure and all the other things that come along with that, right? But yeah, we're definitely doing multi-cloud. And it's always a challenge and we're always reinventing, or not reinventing, but figuring out how things should work as we go. At CNCFCI, we're using a combination of two cloud providers. We use AWS for our front-end stuff because it's a live workload, yet it has a really high rate of change. And then we use packet.net for bare metal for our resource intensive workloads because it has such a low rate of change that it doesn't make sense. So at GitLab, we have a pretty complex story as it relates to the clouds and the environments which we use. So we offer both an on-premises product that you install yourself and self-manage. And you can manage that on bare metal or any cloud. And then we also offer a sash platform which runs the exact same code as our premises product and is the largest instance of GitLab. So that GitLab.com instance actually runs all on GCP. So we had a well-publicized migration from Azure to GCP. And for the most part, that is a monocloud SaaS where that runs completely in GCP. But we also have a component of our CICD build agents which we call runners. And those runners are actually multi-cloud. So those we offer as what we call shared runners. You can just sign up and you can just start using these to run your CICD workloads. And those run both on GCP. And as of 12.5, which is launching this month, you can also do it on Windows as well. So we're launching Windows Beta. So that's multi-cloud. Although you can also manage your own runners. So using our SaaS solution, you can run them on-prem or any cloud you want. And then of course, we have features where users and the users that I talk to all the time are doing multi-cloud. So this is things where they're using, perhaps Terraform to orchestrate this and doing deployments to multiple clouds using GLEB's CICD. This is where we have a Kubernetes integration with GKE. And as of 12.5, releasing this month, we'll also have an EKS integration. So that is multi-cloud. And then you also heard about our cross-plane capabilities which are shipping in 12.5, which allow orchestration across managed services. So a complex story, I think, if you caught all of that. So at Genworth, we're using a combination of some on-prem solutions as well as AWS and Azure and then a couple of SaaS and PASS cloud-native solutions as well. And for us, multi-cloud is not necessarily a choice due to the regulated nature of the space that we're in. There's certain things, there's certain products that we have to, you know, the regulation, whether it's external or internal, kind of dictates where we actually have to run certain workloads. Thank you. Before we actually go to a question, I can also share how we use multi-cloud and then use CICD. We had two projects. One is Open Source, Open EBS. The other one is a SaaS platform called Director. Both of the CICD is done using GLEB. And the runners, as Williams was saying, they actually need to certify this project before it actually gets shipped on multiple clouds. So we run the runners on multiple clouds. One thing that we also make sure is you keep the agnostic piece of the stages separately and then cloud-specific tasks separately. I think we're going to talk a little bit more about that in the panel. Before we actually talk CICD, why don't we recap what is multi-cloud and what are the advantages? And specifically, are there cases where multi-cloud is not a good scenario to use? Maybe Alex? Yeah, so I would say obviously, as computing is becoming more and more modern and changing, you definitely have to have capabilities to enable your customers to run through software in whatever platform, right? I don't think there's any more of these excuses where, oh, we're only Windows or Linux or Mac anymore. And it definitely makes sense to build out that capability, but there are challenges, right? I saw an earlier briefing called a briefing here earlier about cloud-plane, right? That's a pretty cool project that I didn't know existed. I'm gonna go research that a little bit more. But those are the kind of changes, I think, that are coming that we need to start looking at so that we can, again, bring that capability. And it doesn't matter where the applications are running. The other piece to this, though, is what you said, the contradictory pieces. When you're running in multiple clouds, that also introduces problems, right? Especially for operators. And I'm talking more specifically about HA, high availability, and also fault tolerance and then disaster recovery, right? These are things people just think about, oh, we need to connect, integrate. But at the end of the day, if you're serious about running these applications, you need to also think about those things and introducing those complexities from the different cloud providers will definitely impact your operations. I've, trust me, from experience, I worked in the government before and we had all those problems. So it always, you know, it's stung me in the past and I always have that in the back of my brain, so that's some of my insights into it. I think I'll kind of piggyback on what Angel was talking about. I think there's various uses for multi-cloud and we're at the moment where if we're only a single point of failure on a cloud, it's really easy to have some downtime, have an outage and be like, well, it was my cloud provider's fault, but to our customers, that doesn't matter. You as a company, we're down and that affects them. So I think with more reason, we really need to push for more folks to start going to multi-cloud, start looking at hybrid clouds, but then it's not just about coming up with the multi-cloud strategy, it's actually doing a lot of fault injection to make sure that your multi-cloud strategy is working. So when we talk about disaster recovery, yeah, it's great that you say you have AWS and if something goes wrong, you're gonna fail over to GCP, but until you actually go and pull that plug on all your AWS cloud and you're like, okay, cool, we actually failed over and we didn't suffer any data loss and maybe the meantime to recovery was only an hour and maybe that's what your company's okay with in terms of your objectives with your customers, but we get to the point that a lot of folks are still on the, we're implementing multi-cloud, but that's where we stop. We don't really talk about what other obstacles that we get to once we have more vendors in the space. Yeah, I think back to this morning's keynote where we talked about maturity levels and I would even say HA is kind of orthogonal so you could have at each stage as you go on your multi-cloud journey, you could be talking about failover, HADR. I'm even curious in this room, how many, I don't think we've answered this yesterday, how many folks in the room are using more than one cloud today? Okay, so there's most everybody, but there are some folks that perhaps are only using one cloud. You're in the right spot learning about multi-cloud. So I would call that using multiple clouds, but maybe not necessarily multi-cloud. The next stage would be what we would call workflow portability. We're using an orchestration tool, it could be Circle, GitLab, and with that tool you're able to deploy to multiple clouds and I would maybe even call that application portability where you can take the same application and run it on multiple clouds. How many folks have that today where they take the same application and can deploy it in multiple clouds? So a lot fewer folks. I will even ask this, how many folks have the level where perhaps you have the same application and workloads from that application can just span multiple clouds? Does anybody have that kind of sophistication? So our folks that spent two years to go build it have gotten to a very, very sophisticated level, but most of us here in this room are on a journey and so it's early days as a lot of folks have said and I think as we're going, the question to ask is not necessarily binary multi-cloud or not, it's where am I at in this maturity model and what's the next step are the questions? All right, go ahead. I think there's another area that it's really important to have a multi-cloud strategy now and that's testing. There's a lot more applications now that are becoming event-driven and have relying on integrations with cloud providers and it's more than one. You can't just test on one provider and go, well, it works across the board, you need to be expanding your test coverage to cover multiple cloud providers to know that your application actually works and there's no random migrations that got in. Yep. Frank? I will say so I guess I can be the negative guy in the room and kind of touch on where they fall flat here. So, at least in my space, multiple cloud providers can potentially fall short. It's usually around, like I touched on my previous comment, around regulatory things and compliance. So, if a particular cloud vendor has a product that is not compliant with a particular privacy regulation or something like that, I can immediately take it off the table and I need to run a sensitive and that would be in the case that I need to run a sensitive workload out in one of those cloud providers. So, like I said in my previous comment, that's kind of where some of these start to direct where some of these workloads, especially sensitive workloads, can run. Yep. Yeah, that's great. It's actually interesting to see the multi-cloud adoption. I was expecting a little bit less than 50% but most of us are using multi-cloud on the panel as well. So, let's actually talk about the deployment which is the crux of the topic for this panel. Can we just go around the panel and then talk about how have you deployed or set up your CACD pipeline so that your developers could deploy the built images, tested images directly onto the clouds? What are some of the best practices that you've been using? Sounds good. One of the ways that we're doing is that at Gremlin, we help companies avoid downtime. So, we're starting to work with integrations with CICD platforms so folks actually start having a stage that they run chaos engineer experiments. So last year we came up with, or I think it was earlier this year, we had integrations with Google Spinnaker and that allows you to integrate your entire pipeline to now have a stage that allows you to run chaos and that allows your engineering team to basically be deploying code at the same rate that they usually are, but they're deploying it with a lot more confidence and there's another layer that we actually talk about with CICD is that you can actually build a lot more testing around past outages that your company has had or maybe some of the large outages that we've seen around in the industry and building testing around those scenarios from making sure the caching layers are able to handle when one of your services goes down but maybe your caching layer can actually limit out and making sure that if your caching layer limits out, the other services that are dependent on it are able to still continue providing a good user experience. So there's various ways that we're talking about it with our customers and around the community but for the most part we're looking at building integrations that allow folks to have an entire other stage just to run chaos before they get to production. I think one thing that helps a lot when you're working on deploys for multi-clouders to choose tooling that is gonna support multiple clouds off the bat so looking at things like Spinnaker for example or Terraform because one thing you really wanna avoid if possible is ending up with different workflows for different cloud providers because then you're testing with different CICD pipelines it's different code and it's inevitably gonna behave differently and then you're gonna run into weird bugs. Yep. Yeah so at Circle that I don't spend as much time as I should with my operations team but as I understand it, we eat our own dog food, right? So that enables us to make sure that we're delivering quality software. The other piece of that is we do find and I can speak to I guess the runs that our customers do and we do have customers that are deploying to multiple platforms. We have a wealth of data. We've been doing this for like nine years so we understand with the metadata we're not looking into the code. I just wanna preface that we're not looking at the sensitive stuff but we do a lot of analysis on the data that we get from the performance of the pipelines and yeah we can see how often people are deploying to the different cloud providers and I was also shocked because there's quite a bit of companies that are doing this to the different cloud providers but as far as Circle is concerned we encounter the same problems that our customers encounter and that's how we deploy multi-cloud. All right probably I can switch one topic before we go to the audience. Multi-cloud is all about being cloud agnostic, right? So you want to be able to develop and deploy it on any of the cloud providers and CI-CD is a pretty important tool in that or area in that but the cloud providers themselves are having this CI-CD solutions. For example, Cloud Build from Google Azure Pipelines. Are you going to get stuck yourself into one of these clouds?  Can we just have some comments? I know. I can start from that side. So, yeah, I got that question earlier and I was thinking about it. For the most part, I think CI-CD platforms in general have to remain kind of agnostic in a sense, right? The syntax is where, like, how you control that automation is where we kind of stumble, I think, as a whole as an industry. You know, we've kind of settled on YAML as like the cloud syntax, right? I think that's fine but on the other side of the house, people want to do more extreme things inside of their pipelines. Now, I don't know if that's the right answer, you know? If you want to put logic into YAML, that's pretty risky. I've seen, like, Ansible's a good example. They have a little couple of control planes there for logic. But at the end of the day, I think, definitely we struggle with being agnostic. Everyone does things differently.  I think YAML's not, in my opinion, YAML's not the best, but it's one of the better ones out there for folks to kind of have an even playing field and then you can expand on that or extend that. It sounds like a bit of a controversial question. We had the cloud providers up here earlier and so now we're asking the non-cloud providers the kind of the vendor agnostic CSD tools. Hey, are you better than the cloud providers? So from that, I was encouraged a bit from what I heard earlier, that I think the answer to that question will be, we'll see. You know, for example, I know that, as I mentioned, GitLab is not just shipping a cloud agnostic tool where folks are using it to deploy, but we have tight integrations with GKE. We have tight integrations with EKS. We partner with all of the clouds, as Brandon will tell you if you see him around here. That's what we consider a strength, is not just the cloud agnostic functionality, but the cloud partnerships we have with all of the clouds. So I think that'll be incumbent. I think if you start to see out of the cloud provider specific CICD tooling that they have tight integrations to the other clouds, okay, yeah, maybe it'll work. But I think that that is the key component, as Denver said, that you want something cloud agnostic that is gonna keep your workflow the same regardless of which cloud you're deploying to. Right, the workflow and then keep the platform specific, there's always going to be platform specific code. Just keep that separate and then, you know, you're actually amuling the logic, keep it agnostic. So it really depends on how you as developers adopt the best practices around multi-cloud. That's what we do. We've got about five minutes. Some questions we can give for our patient audience. All right, audience questions.  I write YAML daily, probably, as well. Yeah. All the time. We use CICD quite a bit. Thank you. What are some of the common use cases you guys are running into that are problems that solution providers should be solving for in this space that you're seeing repetitively? Up time. Lately, it's been a struggle, I think, for some of these cloud providers and, you know, it fails for some folks, doesn't fail for others. So yeah, that's one of the struggles I see, you know, from the platform's perspective. And again, getting back to the integration points where, so yeah, if just to the day GitHub had an issue that impacted all of our customers, right, or most, I should say most of our customers, and it was out of our hands. We were definitely like, wow, this is bad, but, you know, and we're working to fix that, right? So becoming more of a virgin control agnostic, we're gonna be having connections into different virgin control systems like GitLab and others, right? But I definitely believe that these integration points need to be monitored a little bit better and also have, and again, going back to kind of like, failover, getting the ability maybe to say, all right, well, our code's here, but we also have it here, and let's automatically fail this. I always encourage people who are writing pipelines in our platform to do some checks against APIs that they use so that they can just fail their builds right away instead of, you know, wasting money and effort in going to a build that it's gonna eventually fail out of your control. I think with that, definitely having a little bit of a checklist of what it actually means to be production ready and having a lot of that failover testing where it's like, yeah, it's cool if you actually implemented the two clouds, but if you're actually not running these exercises weekly, monthly, at least once a quarter, you won't know until you get paged at three in the morning and your engineers are gonna be pissed, because maybe even that runbook has not even been updated and you're just kind of praying to all the runbook gods that your failover is actually gonna work when you really need it, so making sure that you're actually implementing and running some of this stuff as we wait for more uptime to be provided by the cloud providers. I think that's kind of like where I see it. Yeah, that's a terrific question. What are we seeing that tools should be building to offload from practitioners? And I can think of two. So one is the whole pipeline. You shouldn't have to build a pipeline. What if we just built the pipeline for you? You could just click a button or you could just commit your code and the whole pipeline was already built. At GitLab we call this autodevops and there's a certain set of use cases where this works really nicely and so we think that you shouldn't have to build a pipeline from scratch.  And the other one that comes to mind is orchestration. So when I'm talking to customers the most that are doing users and GitLab customers that are doing multi-cloud, they're doing a lot of orchestration and abstraction. So for example, whether they want to use Google Cloud SQL or RDS and they're having to write an abstraction layer in order to homogenize a logic so they're basically building an interface so that their developers can just say, okay, write to state and then whatever's on the backend is abstracted. And that's a lot of code that a lot of different companies are writing. And so a lot of folks have talked about cross-plane today when I see this type of capabilities and cross-plane and that community emerging, that's pretty exciting because that's what I see a lot of folks writing all the time that could just be pulled out into a tool and offloaded so that you can focus on the business logic. Yeah. I can probably add one more though I'm a moderator but I directly have real-life experience. Uptime is pretty important but fact is the cloud will fail at some point of time, right? So it's very important for us as developers to have the API to actually inject platform failures, right? To see how your pipeline really behaves when the cloud fails, right? So the cloud providers, some of them have, right? So how to create a disk loss, network loss, node loss but not all cloud providers maybe, it's as easy as other clouds. So it'll be good to have some kind of an API emerging on platform failures, that's my take. Awesome, that question really got the panelists going. So thank you for asking it. Any other questions? Oh, sorry. So I'm gonna ask Anna this question but everybody's free to answer it specifically because of your chaos engineering experience which is a sweet job title by the way. So I'm kind of like wondering, because I'm thinking like how I might start with chaos engineering and my first question would be like, well, what kind of tool do I use to kind of like orchestrate these tests, kind of gather the results and then like judge the results because when you're inducing failures it's kind of like it's not like a test pass fail necessarily scenario, it's kind of fuzzy. So I'm curious if you could speak about some of the tooling that you're using to do your chaos engineering. Yeah, so I'll start off that I work at a vendor that is a resilience a company that offers a chaos engineering platform. So we actually offer a free offering of our tool which allows you to run shutdown and CPU experiments on your hosts and your containers. And we actually just launched a pretty neat Kubernetes new product today. And then on the enterprise side we also have various attacks that include like more on the network layer, like latency, blackholing, packet loss, maximizing your CPU, your disk, your IO, your memory. And we have that tool that allows folks to do it but prior to you actually even building your own tool going to open source or using Gremlin there's a little bit of a culture that needs to come with it where you first have to embrace failures. So having a little bit of a blameless post-mortem culture is one of the big things that you should be having. And then we think about chaos engineering in a way that is very thoughtful and very planned. So it's not about just going into your company the next day and be like, hey, we're gonna do chaos in production, let's go. We're gonna bring down some instances, we're gonna shut down some clusters, that's not it.  If you met those abort conditions, you wanna go ahead and halt that experiment, go fix your application, make your infrastructure a little bit more resilient and do it all over again until you can kind of pass it again. And we talk about the blast radius where you don't wanna run this on 100% of your fleet, 50% of your fleet, if you don't know how it behaves on one cluster, one node, one day mindset. So starting really small is the key to success for chaos engineering. I think it's called game days, right? Game days, the culture is really important. Just to add, you can also take a look at the open source chaos tool, Litmus. Point out of that project, it's chaos engineering for Kubernetes, specifically for cloud native applications. It's a little bit of an early stage, but I think it's going to get there. Yeah, because I might say, how do you get started with chaos engineering? Don't, so, but to Anna's point, right? It's about building a culture. So for example, before you can do continuous deployment to multi-cloud, how about figuring out continuous deployment and DevOps for one cloud, right? How about getting a good DevOps culture of small changes, repeatable, boring deployments? And when you have that done really well, then you can think about multi-cloud. In the same way with chaos engineering, you need to be able to have enough instrumentation, monitoring, rigor, blameless postmortems, even to understand what is caused by the chaos tool and what's actual failure, right? Because chaos will help you build resiliency to test if this goes down, does it fail over? But if there's actually something wrong, if you need to troubleshoot, there's not enough memory on this node, and it's not just that the node went down and you need to fail over. This is, I have an incident and I need to go add more memory or add more compute. If you can't tell the difference between those things, then it's not time to jump into chaos engineering. You need to build that culture first. Well, I think, do we have more questions? We'll take one last. Anyone? All right. Thank you very much. Thank you so much, Panel. And moderator, that was amazing. All right, thank you.


So the beauty of being up for level resident is now I get to give you a grade on your rotation. Let me tell you of what things you should not do. Hey guys, welcome to another episode on the TMJ show and the empty journey channel completely dedicated to helping you succeed on your medical journey and doing it with less stress. If it's your first time here, my name is Lakshman, internal medicine resident, been making videos, blog posts, you name it for the last two, three, four years now, crazy. But here on the channel I make content on how to study better, how to get better grades, how to be more productive as well as how to crush it on your clinical rotations. So if any of that sounds interesting to you, then definitely consider hitting that subscribe button and hitting that like button to support the channel as well as getting more videos just like this one in the future. But today I want to talk about a few things you should not be doing on your clinical rotations and this is from personal experience because now as an upper level resident, I get to give that grade of an honor, high pass, you know, near honors, whatever grade your institution uses. I want to give you a few things that I've noticed even in my short time of being an upper level resident that really have cost some med students their grades and hopefully you can use them to actually increase your chances of getting that honors and a high grade on your shelf exam. And at the very end of the video, we'll also talk about a resource to help you crush every phase of your clinical rotations and ideally get both the honors as well as into your number one residency spot. So stay tuned. And one of the worst things that you can do to cost yourself a high grade on your clinical rotations is having terrible presentations. Now I'll give a few examples of where med students struggle. One of them is that they forget that the presentation is their opportunity to shine and they don't give the right proportion of attention of where they can really show off their knowledge to where they can kind of speed up on things. So a few common characteristics of a typical med student presentation is that they're long, they're not informative, and most importantly, they don't highlight what that med student knows and how they want to use it to manage the care of the patient. And that just ends up wasting time and not really leading you to a higher grade. And a few things that I've noticed that really make bad presentations is that some med students will just quickly go through everything. I had an experience where we had a med student on one of our rotations who clearly knew what we were going to be doing for that patient. They knew the plan, they knew the history, but they just rushed through everything. They were almost talking as like a very fast robotic tempo and they weren't slowing down on where they wanted to show off their knowledge. So it didn't matter if they were giving a piece of information that was irrelevant or important, they set it at the same speed. And one of the most important things you can do to yourself and for yourself on your presentations is when there's a piece of information that you really want to share and show that one, you know what's going on, two, you know what that means for the care of your patient, slow down. So for example, if your patient's first primary problem was shortness of breath, then when you present that problem in your assessment plan, make sure you take your time of explaining your thought process, what you think the patient has, why you think it, what you think the patient also doesn't have, and then why you made certain decisions in their management. A lot of times in my experience, I find that the med students will go just quickly list out everything that they've seen their residents tell them that they'll be doing or have seen in the note that the resident has already written, but they aren't able to highlight this is what's important and this is what's not. So for example, if you have a patient with a low blood count, they have anemia and you're not really sure why. The most important part of that presentation is explaining what your differential is for why they're anemic and to what you're going to do to work it up. But sometimes I find that the med students will quickly go through their differential and their workup and then also spend excess time talking about things like, well, if they're hemoglobin is less than seven, then I'll transfuse them and XYZ will trend them with CBCs. But honestly, those are things that you probably read in somebody's note or you written in yours and they are not important for your presentation. So next time that you give a presentation to your attendings and your residents look through your presentation and focus on where the money spots are, what are the pieces of information in the HPI that are going to contribute to your final diagnosis, they're going to contribute to the final management suggestion that you have when you present the patient. Those are parts that you should slow down on and other parts that don't necessarily fit in those money regions are going to be things that you should be able to quickly go through or not even have to say at all. And my final personal gripe about patient presentations, try saying that eight times in a row is really that med students start to find themselves in a reporting phase. I mentioned this in previous videos, but the most important thing you should do when you get a new patient or even if it's an old patient that you've been taking care of for some time is ask what do I want to do for them before you start working on your HPI or subjective and your objective data. If you can really master your management, you don't have to rely on the notes and the things that your upper level residents will tell you instead, you'll say, well, for this problem, I see that this is happening and this is what I want to do and then focus on the things that don't require a lot of mental energy, including working on their HPI and their objective data. So definitely keep working on your patient presentations. If you're struggling, I promise you, if you can suddenly increase the quality, how quick you are, how concise you are, but also make sure you're highlighting where you know what's going on, you're going to be able to increase your chances of being in honors. I can really dictate the students who get honors from the students who don't base off just their presentations alone. And number two is not offering to help. Sometimes they feel like the med student is waiting for me to tell them what to do. And in some regards, that is the proper thing to do, but always look for an opportunity to help your team out, especially if it's your patient. One thing that I often recommend you do is keep a list of all the different things that are on the to do list of your intern and your upper level resident. You obviously may not be able to take care of all of them, like putting in an order or calling a consult or calling a family member if it's kind of outside your wheelhouse. But if there's something special like checking on the patient at later in the day or calling social work or working with the PTs or calling a family member for your residence, then you can definitely add that to your list. And then you can tell your interns like, hey, I can take care of A, B, and C. And sometimes to define that the students who are the most enthusiastic about helping the team without being a suck up, don't do that, can definitely increase their chances of getting honors. Because sometimes I can look past your lack of clinical knowledge for your ability of enthusiasm and ability to help both team as well as the patient. So if you're sitting in a corner doing your UL questions, studying for yourself exam, make sure before you do it, you always ask if there's another opportunity that you can help your team before you take some appropriate time to work on your own. And number three on a similar note is not being your patient's advocate. As a med student, you have the most opportunity, the most time of building both relationships for poorer, as well as the ability to see your patients multiple times a day. Your interns can be busy taking care of all the patients, your residents can be busy supervising the team. And you're going to honestly have the most amount of time to see the patients specifically in the morning, during rounds, as well as in the afternoon. So use those opportunities to ask yourself, does the management that we did for this patient earlier, is it working? If they're in pain and we started them on a new medication, is it actually having a difference?  But it doesn't happen if you only see them when you have to, which is before rounds and then during rounds. So be your patient's advocate, always see them throughout the day. I like to say that if you're coming back from lunch, quickly just lay eyes on all your patients, make sure everything is good, and then come back and report if there's anything worth reporting to your interns and residents. I know personally, if I have med students who'll just kind of independently check in on their patients, it really helps when they tell me, Hey patient, so and so is feeling a little bit nauseous, maybe we can schedule their Zofran instead of just making a PRN because I don't think the nurses are getting it. Those are very small instances that I'll remember that this medical student really cares for the care of their own patient. And again, it just elevates their chances of getting honors. Obviously, they have to have the clinical acumen, all those skills that they're required to build. But those kind of things just kind of raise your chances of doing so. Number four is being inefficient. Do not be an efficient med student. When you're first starting, obviously, you're going to be learning the small skills of how to write better notes, how to present quicker, how to see your patients quicker. But always ask your interns, your residents of like, Hey, how can I do this faster? How can I look at this problem, the situation and being able to do it efficiently, but effectively, I've been through numerous experiences already where med students have been staying till very end of the day, still working on their notes. And if they only have two patients, sometimes it shouldn't take you till five or seven PM to work on your progress notes. Always ask how can you make this faster? How can you make every experience a little bit more efficient? That way, then you have more free time to one study for yourself exam, which you should and two, being able to help both the patients as well as your team kind of further the care of that patient. If you're noticing that you're slow on a certain task, always ask for advice on how you can potentially get better and more effective doing it. And on that note, if you want more tips for your clinical rotations on being more efficient, being more effective, I'll link down below a full playlist that we have on YouTube. And finally guys, the most important thing that will cost you a high grade and a mistake that you can make on your rotation is a lack of professionalism. Now professionalism includes a lot of things. Number one is showing up on time. So don't show up late. If you show up once, make sure that you text your upper level resident, your intern to let them know what happened and that you're going to be a little bit behind, but don't make it a repeat process. Two is making sure that you are having proper conversations with your interns and residents. Sometimes med students get a little bit too comfortable and sometimes they're on the opposite end.  And they're your mentors and they're people who you can look forward to advice, but don't try to make them your friend. You can be friendly, but sometimes looking at your upper levels as a friend can lead you to say some things that maybe you probably wouldn't have said otherwise. And I'll just leave it at that. I've had some med students say some inappropriate things, whether it's about their grading, whether it's about patient care. You just don't want to have a chance of that being on your final evaluation. So always be professional with your patients, your attendings, your team members and make sure you show up on time. Get a watch. And finally, guys, if you want more resources to help you on your clinical rotations and if you are nervous, if you haven't started or if you're on your rotations and you're struggling, then definitely check out the crushing clinical program that we have on remedy journey.com. I've had a lot of students go through the program already and they found that one, they've increased their chances of doing well on their shelf exam, which is super important. But two, they've also increased their chances of getting honors on their rotations. I haven't definitely had some students who've been able to crush all of their rotations, get a 4.0, but most importantly, set themselves up for getting a number one residency spot. So I'll link down below the crushing clinical program if you guys are interested, but that's going to be on this video on what mistakes you should make on your clinical rotations. I'll keep making more videos like this as I go through my upper level training and realize other common things that I find in my experiences, but also make sure you comment down below with any questions you have about your clinical rotations, any tips that you would like. I'd love to make more videos or just specifically answer your questions down below.  So I'm waiting. Cool. And also consider if you're watching this, you made it to the very end, hit that subscribe button to get two videos at least like this one every week. But thank you guys so much as always. Again, all the resources that I mentioned this video are linked down below. Hopefully you guys will check them out. I appreciate you making it to the end of the video and the support. Thank you for always being a part of my journey. Hopefully I've been a little help to you on yours. I'll see you guys in the next one. Peace.


Soldiers with the 299th Engineer Battalion, a reserve battalion stationed at Fort Belvoir, Virginia, put on a show for military leaders from Brazil and the U.S. Army Corps of Engineers. The soldiers demonstrated their capabilities in providing mobile electrical distribution, utilizing specialized engineering equipment, as well as their bridging capability to deploy a floating improved ribbon bridge. The demonstration is part of an annual visit between the two chiefs of engineers to enhance theater security cooperation in military engineering. Today was all about showing some unique pieces of capability, engineer capability, excavators, our bridge erection boats, right, and also micro grids that the Brazilian engineers are looking to modernize in their own forces just like we are. The demonstration caps off a week-long visit by General Julio Cesar de Aruda, the Brazilian Army's chief of the Department of Engineering and Construction, where he visited USACE's Mississippi Valley Division and Engineering Research and Development Center, both in Vicksburg, Mississippi. We learned a lot here. This cooperation with the engineers. There were many aspects that we wanted to learn here, and we have learned a lot through this visit. One of them was on Waterways Navigation, Mississippi River, which was the beginning of the visit, and it was very productive and very important for the Brazilian Army. And besides the visit with the waterways, we've also learned a lot in other areas with the Corps of Engineers and Department of Army. We're very pleased with the visit. The leaders say visits like these are important to continue to build regional partnerships that look to enhance interoperability while developing the potential for increased regional response capability. The US and Brazilian armies have worked together for many years and are continuing to seek to advance the partnership beyond the high level of cooperation already in existence with future meetings in the works. From Fort Belvoir, Virginia, Patrick Bloodgood.


Tina Fey returns to her beloved and iconic classic Mean Girls.  Because I wanna experience torture.  I can't wait to start. Let me first say I love Tina Fey. 30 Rock is one of my favorite sitcoms. It's a top 10 for sure. It's brilliant. Her writing is great. I love her performance and some of the SNL stuff she's done. She's great in the first Mean Girls as the teacher and now she's back again as the same teacher and so is Tim Meadows and that's about it. Why isn't Amy Poehler the mom again? Was that too much to ask? They're like best friends in real life. Who cares? I'm actually glad Amy Poehler didn't come back because this movie is garbage and I wanna say for the record I love the original Mean Girls and yeah I'm going to be pitting this against that one because why wouldn't I? Should I pretend the original? This understands that it exists. This is well aware. It makes several comments. It updates some of the jokes to be more modern but also be like yep we kind of went there before.   There's singing, there's dancing. After all Miss there is Francine and there's lots of songs and I will say a good chunk of them are fun and catchy although they undercut them a lot by stopping the performances 25 to 35% of the way through and then having dialogue for a while and then going back to it for a second. Most of the songs in this movie feel like they were cut way down like there was a lot more to do but they decided not to do it. The movie already feels long enough already. It's two hours too long for a comedy. I like them right around an hour and a half and I know the original Mean Girls is pushing a little too long too. The characters are just trash in this okay? They are terrible in this and it's not the fault of the actors. They're doing what they can. The only one that's actually decent is the main character Katie. She looks good. She sings well. She plays the performance fine. Just kind of a fish out of water type of individual and that's good. She's good at it.  I don't know if there's if the relatives if she kind of did some sort of a freaky Friday with Amy Adams at some point recently and took her face and her body but made it a little younger. I don't know what's going on but she really reminded me of Amy Adams in this film. Good performance from her fine. The plastics.  Were they trying to get the worst people they could to play these characters? They're doing cosplays. Regina for instance. What this is this character just sucks in this movie. What made Rachel McAdams work so well was she was sassy. She was beautiful but she was also funny.  That's how Regina was. She was saying bitchy things but she was doing it with gusto. She was doing it with a pageantry that just really sold me on it and made her funny all the same. This new actress doesn't have that. It comes off as just mean. Just mean for the sake of mean and then at some points when I feel like she should have been mean she kind of held back on some of it so it just was very inconsistent. The other two were so bad. One of them all she does is she kind of has her eyes really big. The Amanda Seafreed character just stands there most of the time. Doesn't even say anything. Just I'm dumb.   She had the full chest on display and that was the entirety of the song was basically just look at my tits. It was uncomfortable and weird. It was just it was kind of an odd scenario and if you saw the movie you'd understand what I'm talking about. If you didn't that's good on you because there's no reason to watch this movie unless of course you fall into the bucket of people that doesn't care that everything's being remade.  I don't know why we have to keep going back to these wells outside of it makes money and I love Tina Fey so it just hurts me to even think this way but that's how it is. I was watching this movie and all I kept thinking was this was so much better before. The way they said these lines didn't hit the same. These actresses feel completely out of place almost intentionally miscast to be worse. What is the point of any of this? This also reminds me of those terrible episodes of sitcoms and I know some people are going to like these ones but I think say by the bell I think scrubs episodes where they do musicals in the episodes almost always are awful to me so it's very much a personal preference but when they do a musical episode of a tv show I usually hit the skip on the on the remote for that one like yeah no I don't need to see the off pitch or weird acting and singing and terrible choreography. To the point of mean girls the singing is fine like it sounds good the choreography is pretty fun. I did see glimpses of brilliance from Tina Fey in some of the dialogue there were points where I was like oh that's a straight up 30 rock joke where she where she starts to go somewhere and then she hits you with something else I like that but it's so far and few in between. My personal beef aside what can you expect if you are actually looking forward to this movie? Again there's a lot of music it's very colorful cinematography solid it looks good there are some decent camera shots where they kind of pretend they're one takes but I don't think they are they're just doing a little bit of trickery but for the most part it's pretty seamless I just I don't know what else to say like I don't know how to get people on board and I don't really think that's my job I'm just a movie fan okay I have another job this is all just for fun and it's a side income but by no means you know I'm not making millions of dollars here okay so I'm just being straight with you this is a film that's modernized so if you're triggered by you know sexuality if you're triggered by more than two genders you're gonna want to burn this thing to the ground because it will offend you in that sense this is very much like you know 2024 the whole rainbow spectrum thing I don't give a shit about any of that I'm just looking for an entertaining good movie and this really doesn't deliver for me because I'm just so upset watching it because there's another movie that's better than it's at my house like I went out I wasted a half hour driving to the theater to watch this and I wasted two hours to watch it plus trailers plus like this is a four and a half hour day gone down the toilet just so that I can bring it to you just so I can tell you my thoughts on it at first I thought you know what maybe this will be different enough they'll go a different direction with it that I can look past all the weird acting choices and some of the bad dialogue but no it really is beat for beat the same exact movie with a ton of the same lines I mean it's just all played out and the scenes that are iconic from the original are done a little bit differently and they're never done better so it's it's again it's okay it's a musical version whoopity fucking doodaw this is where I'm at now in life let me know I have I mean I'm done I have nothing else to say about this movie if you saw mean girls and you loved it if you thought oh wow what a fresh fun spin they modernized it they pulled in some of the original dialogue and some of the characters great that that's good for you I don't care I'm glad you liked it you got your money's worth I'm just here to to maybe scare people from not seeing it if they were on the fence or maybe to push people towards seeing it if that sounds interesting to them maybe it does and that's that's cool I again not not really a big deal to me whether or not you like a movie and I hope it's not a big deal if I like it or don't let me know though please subscribe if you haven't I post tons of movie content each and every week love to hear your thoughts would love to see you stick around like the video share it do all that crap I appreciate it I'm like so I'm so pissy I don't why whatever do whatever you want I don't care anymore no it's fine it's a movie I move on all right take care


In the previous lecture we have discussed various laws which govern us to calculate the probabilities of various events. One thing that we notice that when we are discussing the raw sample space many times it is quite difficult or you can say complicated to look at all the possibilities and then look at the manifestations of various events. It may happen that it may be helpful to look at only the numerical values of certain variable. For example, let us consider the game of a say a basketball match. Now at the end of the match we will be interested in the total number of the baskets which were put successfully by both the teams and that would give the winner of the in the match. In the early in a game of tennis and at a game of badminton and so on where the outcome may be simply a number for example, in a game of badminton the final scores of the three games or five games or in a game of tennis the final scores of best of three games or best of five games etcetera. So now the entire duration of the match is not important which point was one by which player that is not important ok. That means ultimately we are associating certain numerical values with the phenomena or you can say outcome. Now this association if we formalize for all values of the sample space we call it a random variable. So let us formally define what is a random variable. So let omega Bp be a probability space a real valued measurable function defined on omega this is called a random variable that means so now usual notation for the function in mathematics is F, G, H etcetera. However here it is a random variable so we call it as a x, y, z etcetera. So we use a notation for example, x is a function from omega into the set of real numbers at the same time we put a measurable condition. By measurable we mean that if we consider a sigma field of subsets of R then the inverse image of any of the set should be an event here that means it should be a set here. Now typical examples let us consider. So consider five hits by or five shots fired. Now out of this x could be the number of successful hits to the target. In that case see when the five shots are fired at a target then the sample space may have the possibilities like all are successful. So you may have four successful and one missed and so on all are missed these are the possibilities. However x can take only values 0, 1, 2, 3, 4 and 5 and so here you can see that looking at this one is quite easy and convenient. Let us take some more example suppose we are considering the number of bulbs operating after say 2 months. So now this could be for example there may be there are say total 100 bulbs then how many of them will be operating after 2 months. So let us say x is the number here then x can take values 0, 1, 2 up to 100 and we may look at the probability distribution of this. We may look at the life of a bulb. So in this case it could be some numbers say from 0 to infinity or it could be 0 to 100 and so on. It can be depends upon the way we try to use our sample space. We can consider say waiting time at a traffic signal. Suppose this is y then waiting time can be anything from say 0 to 3 minutes suppose the timer is set up up to 3 minutes then it could be 0 to 3 minutes. The values possible values can be any value between 0 to 3 etcetera. So here you can see that in each of these example we are having a numerical value from the sample space that means each element of the sample space is allotted a numerical value. So this is called a random variable. Now based on the type of the values for example here I am assigning the values 0, 1, 2, 3, 4, 5. Here I am assigning 0, 1, 2 up to 100 and so on. Here I am assigning the values on an interval. So depending upon that we consider the classification of random variables classification of random variables. So the classification of random variables is one is discrete random variable. So if a random variable takes finite or countably infinite number of values then it is called a discrete random variable. For example if you look at this random variable this is a discrete random variable that is a number of successful is to the target. So I consider number of attempts to clear a competition. So a person may be allowed a finite number of attempts to clear the competition. So the values that the random variable may take 1, 2 suppose up to n number of trials are allowed. So you can have 1, 2, n as the number of values of y then continuous random variable. If a random variable takes values over an interval it is called a continuous random variable. So for example waiting time at a traffic signal I am putting 0 to 3 interval or life of a bulb 0 to infinity etc. So this is example of continuous random variable. For example life of a bulb waiting time at a traffic signal. There are also random variables which are partly discrete and partly continuous but that distinction will become clear when I give the probability distribution of a random variable. So let us look at the probability distribution now. How do we define the probability distribution of a random variable? First of all let us look at the origin of this one. See whenever we have a random experiment from the random experiment we have a sample space and a certain assignment of probabilities can be made depending upon the type of experiment to the various outcomes or to the various events which are there. When we are allocating the values real numbers to those outcomes then the corresponding probabilities are also transferred. Now in a case of discrete distribution this assignment is quite natural but in the case of continuous distribution since we are dealing with the intervals that assignment does not result in a direct transformation. However, we can give a formal definition in the following fashion. So we can consider so we have omega B P as the probability space and when we define a random variable X then omega goes to R this sigma field of events it is also transformed to another sigma field which is a sigma field of subsets of R and in place of P let us say Q. So this is an assignment let us define. So for any set C we define Q C is equal to probability of X inverse C that is equal to probability of B where B belongs to B. So here Q is called the probability distribution of random variable X. Now let us see that how it is done in the real situations when we are dealing with the discrete random variable when we are dealing with the continuous random variable then we will have different ways of this assignment. So let us consider the discrete case here this probability distribution is given the name probability mass function of a discrete random variable. So when it is a discrete random variable the random variable takes values over a set which is either finite or it is countably infinite we can name it by some script X. Let X be a discrete random variable taking values over a set say X which is of course a subset of R. So here X can be since it is finite or countable we can actually arrange the values in this sequence X 1 X 2 and so on. Now the probability mass function of X is a function let us call it P X which satisfies the following 3 conditions. First thing is that P X X i is always greater than or equal to 0. Second is that the sum of all the possible values of the function over X is equal to 1. And thirdly this P X X i is actually the probability that the random variable X takes values X i. Now what is the meaning of this kind of a statement let us explain it further. I wrote here the assignment of a value here. Now this set B is in the it is a subset of omega ok the sample space. So when we are writing like this actually it means probability of all those sample points for which X omega is equal to X i. So this is actually the full description but for brevity we will be actually writing X is equal to X i because probability statement is basically valid for a set on the which is a subset of the sample space. So omega the set of all those sample points for which X omega is equal to X i. So in short we will be writing probability of X is equal to X i. But when the meaning is clear it does not matter whether we write this statement or this statement. Let us explain through an example here. Suppose a shop has 5 say computers out of which 2 are not fully you can say they are not working up to the full capacity not fully operative ok. You may call that they are having some defect ok. A customer buys 2 computers and selects randomly out of given 5 because this that they are defective that is not known to the owner also. Now let us consider X is the number of defectives in his purchase these are her purchase. So now what what are the possible values of X? Since there are 5 out of which 2 are defective and this person buys 2 he may buy both good he may buy one bad one good or he may buy both bad. What are the various possibilities here? Let us look at what is the probability of X is equal to 0. So that is equal to that means he has purchased 3 C 2 that means he has purchased both from the good ones. The total number of ways of selecting 2 computers out of 5 is 5 C 2 which number is equal to 3 by 10 here. This is actually P X 0. Similarly, if we consider probability of X is equal to 1 that means he has purchased one good and one bad. So, the probability here is becoming 6 by 10 that is P X 1 and what is the probability of X is equal to 2 here. So, that will be equal to he has purchased both bad that is 2 C 2 divided by 5 C 2 that is equal to 1 by 10 that is equal to P X 2. So this assignment of values that is P X 0 P X 1 P X 2 this is called the probability mass function of this random variable X here. If we want we can have a basic understanding by considering the plot of this suppose this is 1. So, this is say 0, 1, 2. So, at 0 you have 3 by 10 at 1 you have 6 by 10 and then you have 1 by 10. So, this is can be depicted by a bar diagram actually. Let us consider one more example of the discrete distribution. Suppose a card is drawn randomly from a well shuffled pack of cards. Now, we define the random variable X as follows. If the number on the card is between 2 and 10 its score is that number. If the card drawn is Jack, Queen or King that is a picture card its score is 20 sorry its score is 10 and if an S is drawn its score is 20. So, let us call X as the score ok. I want the probability distribution of X. So, what are the possible values of X here? X can take values if it is between 2 to 10 it is score is that number that is 2, 3 up to 10. If it is Jack, Queen or King then also it is 10 and if an S is drawn its score is 20. So, the possible values are 2, 3, 4 up to 10 and then 20. Now, if you want to find out the probability distribution here what is the probability of say X is equal to 2. Now, that is simply equal to because there are 4 cards which are having the value 2 and we are drawing one card out of 52 cards. So, it is becoming simply 4 C 1 divided by 52 C 1 that is equal to 4 by 52 that is equal to 1 by 13, but this argument will be valid for 3, 4 up to 9. So, actually we can say probability X is equal to J is equal to 1 by 13 for J is equal to 2 up to 9. Now, the case of 10 can be clubbed with Jack, Queen and King because that score is also 10. Now, there are 16 cards which are 10 Jack, Queen or King. So, the probability that X is equal to 10 that will become equal to 16 by 52 that is equal to 4 by 13 and what is the probability of X equal to 20 because that is an S which is again equal to 4 by 52 that is equal to 1 by 13. So, this number I can also combine here. So, ultimately we can write the distribution in the following form we can write. So, the probability mass function of X can be written as P X J that is equal to 1 by 13 for J is equal to 2 up to 9 and 20 and P X 10 is equal to 4 by 13. So, this is the complete probability distribution of the score which is defined in this fashion in this particular problem. Now, if we have continuous random variable it is obvious that one may not be able to get the probability distribution in this fashion because here what we are doing is we are making a simple assignment and since the elements of the sample space have a probability assignment that is directly transformed to the probability distribution of the discrete random variable. In the case of continuous random variable since there are the values are taking over an interval now this type of facility is not there and in that case the probability distribution is obtained either by the rule which is governing by which is governing the process or one may look at the probability histogram of the data that means frequency distribution and then we approximated by a frequency curve. So, let us consider probability distribution of a continuous random variable. In the case of continuous random variable we call it a density function. So, probability density function of a continuous random variable. So, let X be a continuous random variable and when it is a continuous random variable it is taking values over an interval. Now, that interval can be having a closed and bounded interval or it can be infinite from both the sides. So, in general we can consider the set of values from minus infinity to infinity. Now, over the portion where the probability is not there the density function will be defined to be 0. So, we can define in general f x x is probability density function we call it in short pdf of x. If it satisfies that f x x is always greater than or equal to 0 the integral over the real line is equal to 1 and thirdly if we consider any interval probability of say a less than x less than b that is given by from a to b. Now, in this case a less than x less than b we may also consider a less than or equal to x less than b we may consider a less than x less than or equal to b or a less than or equal to x less than or equal to b all of them are considered to be equivalent. In fact, when x is continuous probability of random variable taking a fixed value is always 0 for all c. In fact, this is not the density function in the discrete case this is the probability mass function, but in the continuous case this is not this is this probability is always 0 actually you have a density at c which may be 0 or non 0. So, let me explain it through some example here. Let the let implies of an organization between 9 am to 11 am daily in the office let x denote the time of arrival. Now, here you see that we are having a 2 hour period and it is found that the probability density function of x is given by. So, considering the starting time as 0 the time can go up to 2. So, the density function is given by f x x is equal to c times 4 x minus 2 x square 0 less than x less than 2 and it is equal to 0 otherwise. By otherwise we mean that when x is outside this interval now that is natural because we are considering the arrival timings between 9 to 11 only. So, it is a 2 hour period. So, the probability density function is having a non negative value in this region only outside this it has to be 0. Now, here there is an unknown constant c written here. So, first thing is that let us determine this c. Now, this function has to be positive which we can obviously see it is actually positive between 0 to 2. Now, secondly we observe that the integral of this function to determine c we should have the integral of f x d x is equal to 1 which is equivalent to saying c times integral 0 to 2 4 x minus 2 x square d x is equal to 1. Now, if we look at this integral. So, this becomes simply 2 x square minus 2 by 3 x cube from 0 to 2 into c that is equal to 8 minus 16 by 3. So, that is equal to 8 by 3 c. Now, if this is equal to 1 this means that c is equal to 3 by 8. So, actually the probability density function is now so the probability density function is actually f x equal to 3 by 8 4 x minus 2 x square or we can take 2 common here then it becomes 3 by 4 2 x minus x square for 0 less than x less than 2 and it is equal to 0 otherwise. Now, suppose we are interested in certain probability for example, what is the probability say that half is less than x less than 3 by 2. That means, we want to know that imply arrives between 9 30 to 10 30 time. So, then this is nothing but the integral of 3 by 4 2 x minus x square d x from half to 3 by 2 which of course can be evaluated easily it is x square minus x cube by 3 from half to 3 by 2. So, we can substitute these values here and we can get the answer as equal to 11 by 16. For example, we want to find out what is the probability that x is less than half that means what is the probability that an imply arrives between 9 to 9 30 then this will be equal to 3 by 4 0 to half 2 x minus x square that is equal to 3 by 4 and once again it is x square minus x cube by 3 0 to half. So, once again if you want we can actually evaluate this 3 by 4 1 by 4 minus 1 by 24 that is equal to 5 by 24 that is equal to 15 by 96. You can actually see that the probability of arriving within first half hour is much less the there is more probability concentrated from half to 3 by 2 more implies arrive between 9 30 to 10 30. As I mentioned that there may be a random variable which may take values over an interval and it may also take at a finite number of points in between. Now, what is the meaning of that? Now, here you can see that when we are having a continuous random variable then the probability of a point is 0 whereas, in a discrete case we have observed that the probability assignment is for the points only probability of x equal to x i is equal to p x x i. Now, we may have a random variable which may take positive probability at points and then for points it may be 0 and probabilities over intervals are allocated. This is called mixed random variable. So, let us look at this a mixed random variable. So, a random variable which may be partly discrete and partly continuous is called a mixed random variable. Let us look at some physical example. We have considered say waiting time at a traffic signal. Now, the vehicle is going and then there is a traffic signal. So, we are looking at the probability distribution of the waiting time. Now, one may say that it is an interval depending upon the setting of the signal timing like it may be maximum most of the signals are set up to say 2 minutes, 3 minutes or 1 minute timing. Then you may say the time is from 0 to 3 minutes and it is an interval. But it may happen that when the vehicle is passing or when it is encountering the signal the there is a green light and then the waiting time is actually 0. Now, it may happen that say one third of the time or one fourth of the time or one tenth of the time you actually encounter a green signal. So, there is a positive probability of x is equal to 0. So, you may say for example, waiting time at traffic signal. So, let us call it x. So, we may have probability x equal to 0. Let us say suppose one tenth of the time we observe this and thereafter we may have a density and that density may be having say an interval you have 9 by 10 into say 1 by 10 that is equal to 9 by 100 and you are having 0 less than x less than sorry it need not be it could be some interval say 0 to say theta. So, we may have 9 by 10 theta. So, that means that this is the total length of the interval in which you may have to wait. So, here you can see if I integrate this density f x dx from 0 to theta I get 9 by 10. Now, 9 by 10 plus 1 by 10 is equal to 1. So, the total probability assignment is completed, but here you can see that in this range you have a density function whereas, at 0 you have a discrete point. So, for example, a question may be asked what is the probability that the waiting time is less than or equal to say theta by 2. In that case this is equal to probability of x is equal to 0 plus the interval the integral of the density over the interval 0 to theta by 2. So, 9 by 10 theta dx. So, this is equal to 1 by 10 plus 9 by 10 and then you have half here. So, that is equal to say 11 by 20 here. So, this is an example of a mixed random variable. Now, from this example it is clear that sometimes when you have a mixed random variable it may not be very convenient to consider the probability density function or the probability mass function. In that case we have a more general function which is called the cumulative distribution function of a random variable. Cumulative distribution function of a random variable. So, the cumulative distribution function we can write in short CDF. The CDF of a random variable x is defined by capital FX is equal to probability of x less than or equal to x. As I mentioned actually this is the probability of the set of all those points for which x omega is less than or equal to x, but in short we can write it as a probability of x less than or equal to x. So, the name cumulative distribution has come because you are considering the probability of all the points which are coming less than or equal to x. So, you are adding for example, if you say x is equal to 0 then you are considering all the points which are up to 0 you are considering the total probability assignment up to 0. Then if I say x equal to 1 then further you are adding the probabilities of all the points which are assigned values between 0 to 1 and the previous values are already there that is why it is becoming cumulative distribution function. We will see that this function is quite useful and also it is having certain characterizing properties. Now, certain things you can observe easily. For example, if I say x tends to plus infinity if I say x tends to plus infinity then naturally all the points will be incorporated here. So, this will be actually become the probability of the full sample space and therefore, this will be equal to 1. If I say x tends to minus infinity then naturally this is showing that the no values can be assigned here and therefore, the probability of the impossible event that will be equal to 0. So, similar properties we can write here. The CDF fx satisfies the following limit of fx as x tends to minus infinity is 0. Limit of fx as x tends to plus infinity is equal to 1. Then if x1 is less than x2 then fx x1 is less than or equal to fx x2 that is f is always non-decreasing function. And limit of f h tending to 0 plus that is equal to fx for all x that is f is continuous from right at every point. So, now let us see that what is the relation of this capital F function with the probability mass function in the case of discrete random variable and with probability density function in the case of continuous random variable. Further we also have a point to make that if I have a capital F function which actually satisfies these four properties if that is so, then certainly that function will be CDF of a random variable that is a very striking property here. Conversely if f is a function defined on R. So, R to R basically satisfies the above four properties then it is CDF of a random variable x. That means, we can actually find out a random variable for which this will be the cumulative distribution function. So, now let us look at the relationship that it may have with the discrete and continuous random variables. So, when x is discrete then see we can find out the PMF from the CDF we can given the PMF we can find the CDF. So, both the things can be found out let us see. If I consider CDF then it is probability of x less than or equal to x that is the probability of all those points which assign the value capital x to be less than or equal to x. Since it is a discrete random variable say with probability mass function say Px then this is nothing, but probability of x is equal to xi, xi less than or equal to x. So, that is becoming simply probability of Pxxi xi less than or equal to x. Conversely if I want to find out Pxxi then what it is? It is probability of x is equal to xi. Now if I have assigned my values in the space of values of capital x in the sequential order x 1, x 2 and so on. That means we are saying like this. Then this is nothing, but probability of x less than or equal to xi minus probability x less than or equal to xi minus 1. Then this is simply becoming Px it is becoming f of xi minus f of xi minus 1. So, given a CDF one can find a PMF given a PMF one can find a CDF. Let us look at the example that we did here. In the case of discrete random variable I define this probability mass function. For this one let us consider for the example of defective computers let us consider CDF. So, let us look at this. Now from the nature of the distribution it is clear that random variable does not take values before 0. Actually the values which are taken with are 0, 1, 2. Now this function is defined on the whole real line. So, naturally this probability of x less than or equal to x that is actually 0 if x is less than 0. Now first value that it is taking is at x equal to 0 and the probability for that is 3 by 10. So, actually you can say that it is equal to 3 by 10 if x is equal to 0, but now again you observe that from 0 to 1 further addition of the probability is not there. So, actually this statement you can qualify you may say 0 less than or equal to x less than 1 because up to 1 there is no further addition. Now at 1 you are actually having 6 by 10. So, this probability will be added here this will become 9 by 10 for 1 less than or equal to x less than 2. At 2 you are further adding 1 by 10 and therefore, this is becoming 1. Actually if we plot this it will look like this up to 0 you have 0, from 0 to 1 you have 3 by 10 then from 1 to 2 it is 9 by 10. So, something like this and there after it is becoming 1. So, if on this side we have x then f x is given like this. Now this is further revealing if we look at this function this is actually discontinuous at 0, 1 and 2 and you look at the discontinuity and you can actually look at this is basically jump the values was 0 suddenly at 0 it is becoming 3 by 10. So, if you look at the size of the jump that is 3 by 10 that is precisely the probability of x is equal to 0. Similarly, you look at the jump size at 1 it is 9 by 10 minus 3 by 10 that is 6 by 10 and that is precisely the probability of x equal to 1 that is 6 by 10. Similarly, here if you see this jump size is 1 minus 9 by 10 that is 1 by 10 and that is precisely the probability of x is equal to 2. So, we can conclude that the CDF of a discrete random variable is a step function with jumps at finite or at most countably infinite number of points. Further the size of the jump is equal to the probability of that point. See if this was given we can actually calculate the probability of x equal to 0 by taking this difference the probability of x equal to 1 by taking this difference the probability of x equal to 2 by taking this difference. Let us further consider for the card example. So, for the card example here x was a score and we look at the CDF. Now, you look at the assignment here the values are starting from 2 up to 9 then 10 and then 20. So, there will be jumps at these points. So, you can describe like this it is 0 for x less than 2 it is becoming 1 by 13 for 2 less than or equal to x less than 3 it is 2 by 13 for 3 less than or equal to x less than 4 and so on 3 by 13 7 by 13 for 8 less than or equal to x less than 9. Now at 9 you are again having the probability 1 by 13. So, that is added it is becoming 8 by 13 for 9 less than or equal to x less than 10, but at 10 you have the probability 4 by 13. So, this is actually becoming 12 by 13 for 10 less than or equal to x less than 20, because the next value is assigned 20 that is 1 by 13. So, it is becoming 1 for x greater than or equal to 20. Now, this is a slightly lengthy example, but it is also quite revealing here. For example, you can see the jumps are at the points 2 3 4 5 6 7 8 9 10 and 20. So, for example, if I want what is the probability of x equal to 7. So, probability of x equal to 7 is found out by looking at the size of the jump at 7 that is 6 by 13 minus 5 by 13 that is 1 by 13. Suppose, I want what is the probability x equal to 10 then you look at this at x equal to 10 the jump size is 12 by 13 minus 8 by 13. So, it is becoming 4 by 13. So, that is actually the probability of x equal to 10 that is 4 by 13. Now, if the random variable is continuous then you can see that there will be a slight difference in the description here. If we are having if x is continuous with pdf say f x then by the definition of pdf if I look at f x that is probability of x less than or equal to x that is integral from minus infinity to x f x or f t dt because we have seen the definition in the case of continuous random variable that the probability of an interval is given by the value of the integral of the density over that interval. So, now in this case the interval is minus infinity to x. So, we integrate from minus infinity to x this one, but if we look at this carefully this is actually denoting indefinite integral of the function f and we know that if capital f is defined as an indefinite integral then this will be an absolutely continuous function. And further you will have d by dx of f x is equal to f x almost. So, let us look at the example that we have done earlier. So, let us look at this continuous distribution here. So, here f x is equal to 3 by 4 into 2 x minus x square for 0 less than x less than 2 it is 0 otherwise. Now, if you want to calculate this f x then this is by definition integral of minus infinity to x f t dt. Now naturally you can see that there will be a non-negative value only in the interval 0 to 2 in other place it will be simply because you will be integrating 0. So, for example, if x is less than 0 then this is simply 0. Now if x is between 0 to 2 then you are actually integrating 3 by 4 2 t minus t square dt from 0 to x only. So, this integral as we can easily see it is equal to x square minus x cube by 3. So, this value is actually becoming 3 by 4 x square minus x cube by 3. And when we cross 2 then this will become the full integral and therefore this will be simply equal to 1. So, this value will become equal to 1 for x greater than or equal to 2. Now as you can see you can actually include 0 here or 0 here it will not make any difference because this function is actually continuous function. See value at x equal to 0 is 0 from this side also it is 0 and at x equal to 2 if you look at this value is 1 the value at x equal to 2 from left hand limit and the right hand limit both are 1. So, this function is actually continuous and differentiable function and therefore if you look at the derivative of this you will get this here. So, this is the case in the case continuous random variable the relationship between the CDF and the EDF. Now in tomorrow in the next lecture I will be explaining how this concept of cumulative distribution function is quite useful when we are discussing mixed random variables. Because in that case we do not have to separately talk about the density function and the mass function and the CDF itself will give the complete information. We will further look at characteristics of the distributions such as expectations, moments, moment generating function, mean variance, median and say quartiles, measures of skewness, kurtosis etcetera. So, that we will be covering in the following lecture.


Hi everybody and welcome to Mustang Stadium. I'm Jeff Hemmelt here after the Stevenson men defeat Rosemont College. Five nothing here in Mustang Stadium here with the player of the game, Adam Diabagatti. Adam, two goals on the night. The first one was set up by Alex Vitsum. They're late in the first half. You kind of made a diving header there right outside the six. Tell me what was going through your mind during that goal. All I thought about was just Coach telling me pickle corner. He tells me that every day. I just had to make it happen. Well, you certainly did on that first one. It was a one nothing lead. And then you guys exploded for four in that second half. The fifth and last goal there, a low shot outside the box being the keeper. Your freshman year, two goals and a few games for you. How are you feeling so far?  It's great. I mean, it's just work in progress. Still working on it with the support of both my captains, both Yanya and Reed. Being just still working on it. You know, trying to get to that next level. Through your first six games, you guys are five and one best start for the team since 2010. Has there been any secret to your guys' success or is it just everybody contributing? What's been the big factor for you guys? Hard work and dedication. And the guys are great. The locker room is great. Keep working. All right, guys. Well, Alex, Adam, we appreciate it. And we'll see you guys back here on the 13th against Gwynedd Mercy at home. Between that, you guys have a road game against Lancaster Bible. So continue up to good work. You guys are five and one. Keep it going. Thank you, sir. All right. Adam Diabagati joining us here at Mustang Stadium after the 5-0 win against Rosemont College.