Hello everyone and welcome to JSA TV and JSA podcast the newsroom for telecom and data center professionals I'm Laura Noland and on behalf of the team here at JSA Thank you for tuning in to our latest virtual CEO roundtable our first hundred registrants for today's roundtable will have received a fresh lunch Delivered to your door or a gift card to order your meal. So while you are beginning to enjoy those great meals Let's get things underway As a quick reminder for everyone who has joined us today We look forward to your participation during this event So please feel free to add any questions that you may have right into the chat And as usual for the last 15 minutes of this hour We will move our conversation over to LinkedIn where you can engage with our participants directly Simply type in hashtag JSA virtual roundtables or click on the direct link that will be posted in the chat Once we're over there, we'll answer any questions that may not have been answered on camera Now if you have any questions about upcoming roundtables, whatever it may be such as how to register or how to participate Just reach out to us at our website JSA net By the way, just a reminder to mark your calendars our next virtual roundtable will cover lessons learned from COVID-19 and predictions for the new year ahead and that'll take place on December 10th at 1 p.m. Eastern So without further delay, let's get started Our topic today is best practices for partnerships in next-gen network infrastructure In any given year your next-gen network infrastructure requires a highly collaborative effort between you and your partners to ensure effective execution and in 2020 from the pandemic to the floods to fires and other challenges Relationship management has become critical for business survival It is my pleasure to introduce you to our exceptional Executive lineup who will weigh in on what it takes to develop manage and maintain valuable business partnerships Joining us today. We have Manish Mata VP of marketing for extinet Dean Campbell CTO at Light River Frank DeJoy Vice President Network Development at Render Networks Ryan Barbera CEO of Data Canopy and Bill Steen director of indirect channels and Alliance partner marketing for Comcast. Thank you all for joining us today Thank you I'd like to start off with just a brief introduction from all of you if you could tell us about your company and your role Let's start with Ryan Hi, yes, thanks again for for having us today. He's Ryan Barbera with Data Canopy. I'm the CEO here Data Canopy is a Global cloud services and infrastructure as a service provider We have offices in North America Europe and in Asia and we focus very heavily on hybrid and multi-cloud integration Let's go to Manish Thank you Laura. Good morning. Good afternoon My name is Manish Mata. I'm with Xnet systems Xnet systems is a is the leading independent privately owned owner and operator of distributed networks and We are part of the communications infrastructure We you know we Design build own and operate distributed networks, which include small cells and as we utilize a private a purpose built a fiber network to to to offer services All for the carriers for the M&Os for the enterprises and building owners Okay, let's go to Dean, please excuse me. Good morning everybody Dean Campbell on the River technologies We're a network integrator. We design and build and help our customers deploy telecommunications networks loosely kind of defined as the critical infrastructure so that your telephone companies your cable companies Light rail a variety of networks that you know, we keep the world running on an everyday basis Thank you. Let's turn to Frank now Hi, I'm Frank DeJoy Vice president network deployment Render provides a construct construction management SAS platform that transforms design data into deliverable work tasks Sequence by software for optimal geospatial delivery in the field our platform enables paper and and Eliminates rather paper and manual handoffs from the workflows. So crews in the field can use iPads to very efficiently complete work in real time Our clients include telcos co-ops ISP C lax construction and engineering firms across the US Australia and beyond who are deploying fiber wireless small cell Networks at scale In the US our clients have delivered broadband to over 700,000 homes and businesses. Thank you Hey, let's go to build Everybody Lord. Thanks for having me on so most of you are probably familiar with Comcast I'm part of Comcast business, which is eight billion dollar Division within the larger organization We have around two point four million dollar business customers and have a pretty deep portfolio that we sell through direct and indirect sales channels including data networking voice security video and managed services Excellent. Thank you. Sorry. I got a little choked up off camera there. So thanks for bearing with me We're gonna start off the questions today with the digital age So in today's digital age enterprises have no choice but to modernize their network infrastructure So what are some of the challenges that businesses face when designing and deploying a next-gen edge-ready network? And let's start with Ryan. I appreciate it. Thank you Laura, I think, you know, there's a lot of different issues that organizations can face and I think that regardless of size They're they're pretty ubiquitous We've seen a lot of movement in the last few years away from the more traditional premise-based types of infrastructure and organizations really starting to move to geographically redundant or multi-geotypes of of infrastructure and that that creates all sorts of issues You know, we really break it down into security access Speed meaning how quickly are you able to deploy and or reach those networks and then the cost for doing those things? So as we talk to organizations, what we've really seen is that there is an awareness and a knowledge that There is this next generation of technology that needs to be implemented It's required not just for internal process But for clients as well, which I know some of the other panelists will discuss as they they face that a little bit more head-on But you know, what is the cost to do that? Finding the right partnerships in terms of how you're going to actually integrate Your networks and start that digital transformation and move things away from your existing infrastructure out to the edge How you're bifurcating and cutting apart the different parts of your network? It's it's a complete organizational redesign and that can oftentimes be Intimidating especially for technology folks that have done things one way for a very long time Nobody wants to have what we call an REE an RGE a resume generating event So when we come in we need to make sure that we're we're really working with people and that we're helping them understand The security concerns the access concerns the speed and then ultimately the cost for those types of deployments And Minish would you like to weigh in? Absolutely, so I'll build on what Ryan said. I mean today's workforces is increasingly dispersed. I mean, we've seen we're seeing that It's the pandemic effect that's happened The applications have gone to the cloud the enterprise applications are now residing in the cloud You know data suggests that roughly 70% of of the enterprise apps are now residing in the cloud with You know roughly about 90% by the end of next year. So The Infrastructure to has to be decentralized and this is something that we have focused on as as a company at Externet We've decentralized the infrastructure where the access Part of the network has been has been decentralized and come closer to the user Now the core network is also coming becoming decentralized in in getting close to the user as part of the edge network Now you talked about the next-gen edge-ready networks and and there are five key areas that we feel That we should focus on because keep in mind that the workforce today is highly mobile So the the use of mobile in the net in the in the in the workforce has increased tremendously in the last You know a few years, but even more this year So if you keep that that fixed mobile convergence in in mind And you have to bring in, you know, five key elements here So the first part that we feel is the network scalability So the net network has to scale to make it next-gen the network has to scale. It has to scale to demand Um, it has the the services have to be predictable So so the there has to be service level guarantees that come into play All the service to be services to be predictable You have to build in the redundancy you have to build in the diversity in the in the in the in the network itself in the access layer You have to bring in low latency application so the the network has to go has to be High speed high bandwidth So this is really important When you when you get to this whole 5g world Which we are all going to but the mission critical services have to be below one millisecond So how do you make it? You know ready for mission critical services. How do you make the network ready for the high bandwidth? You know usage that is required in the financial world in the in the healthcare So all of these have to come together and then at the end of it all there has to be secure The network has to be secure. So it has to be highly scalable. It has to be predictable It has to have the low latency the high bandwidth and highly secure So this is all something that's that that are key challenges right now for us You know as an industry as we go about you know providing that end-to-end You know user experience, you know, that's required both in the fixed and the mobile world Thank you Manish Dean. Can you weigh in? Yeah, that's a quick tough act to follow these two guys I did I did want to talk about two points and I think we're all in in the violent agreement here We're talking about how network services are becoming just increasingly Critical to any kind of business out there The workforce is dispersing It's becoming The lifeblood of the business to be able to communicate between your employees to clean your apartments and locations At the same time what we're seeing almost all the businesses under tremendous competitive pressure So they are really beginning to focus on their core competency And what we're finding quite frankly is this this ability to be able to partner with other companies find trusted advisors That can help them through the decisions so nobody gets a resume generating event Um to help them with this new technology with the speed with technology is changing Help them make these decisions help them do the research and put together great solutions And then help them get implemented We're asked every day from customers, you know help us because We view this as critical and becoming more critical to the lifeblood of our company But we simply don't have the people with extra cycles To do the research and help us move forward and keep up with as fast as technology is advancing So, you know increasingly it's you know It's becoming about how good is your rolodex? That's how you keep up your competitive advantage versus can I do it all myself? We find a lot of value working with clients in that kind of role Thank you panelists We're going to move to another thought topic iot devices with three billion new iot devices estimated to deploy by 2023 What steps are being taken to prepare for iot and wi-fi 6 so let's start with them Hi, um, thank you so much Looking at that it's a really interesting topic because I think a lot of customers, you know are very familiar with wi-fi of it, but are newer with the iot side of things And one nice advantage Comcast has is we have a whole company focused on iot called machine q So machine q has been out there for years It is building lots of different solutions for different verticals for different lower technologies and talking to VP of engineering a few few days ago coincidentally He was talking about the new Comcast center that we recently completed about a year or two ago And the 65 story tower Has 2,500 wi-fi gateways in it to serve the people that are you know in the building We have 16 machine q gateways for our iot within the building So the amount of low latency low power Range that is provided by iot is is truly amazing And it's really about you know using the right hammer on the right nail for customers that are looking at How they do inventory management how they do temperature management? And there's so many fascinating use cases where customers are getting Significant savings where instead of going gosh, you know, we have 10,000 mousetraps set up across our warehouse You know which ones pop last night right iot can enable that you can put a chip on there and say oh these six did Go pick those up So there's so much potential there that we're seeing it as is a real opportunity to talk to customers about automation All right, thank you bill manish. Would you like to add? Sure, um laura. Thank you. Um Builds are all the right things, but i'll just build on this in in in in terms of what we are seeing out there from an infrastructure perspective When people talk about iot they talk about internet of things um And and our CEO jim hide when he joined about a couple years ago um He talked about the the the real iot is the infrastructure of things and this is something that we've kind of built into our into our Into our motto here and in within the company is we have to build the infrastructure of things the real iot Before we can do the internet of things And while while we see A lot activity a lot of activities going on a lot more has to happen So in a lot of the in in a lot of the industries today When you're building the in building network if you may Whether you're in the industrial side or you're in the health care. It doesn't really matter For iot to happen the networks have to be built from within And when I say the network to again go back to my previous Comment about mobile networks the mobile networks which has wires attached to it the fiber that comes into to attach to it That becomes really critical to actually enable that whole internet of things, you know the the the iot That network has to be built from within and has been built today But it has a lot has to happen today to make that work So now you talk about the edge and how does that plan right? And and and you talk about the building management systems for instance um There is a a need for data collection to happen for iot to work And that really means there has to be a high density of sensors, you know in place for the data collection to happen And and the high density of net of sensors requires a high capacity network within Um the building or buildings campuses When you then then you have to look at how does the data get controlled and for the data to get controlled You need a dispersed, you know set of sensors in the in the facility and for that you need coverage in the network At the end of the day, it's all about the data engine the edge has to be has to be closer to the user or to the end You know usage, you know, whatever the use case is happening For the for the for the system to really work and and right now We are in very early stages of building this infrastructure of things, you know for the future Thank you infrastructure that provides strong investment protection Is imperative to support today's needs and in the future unpredictable demands What types of solutions are you recommending that are scalable flexible and limit business disruptions? Let's start with bill Yeah, I think I have a couple thoughts on that. I mean one of the things that we're currently seeing is Um as we rolled out our stn platform three four years ago We built it over the top so that customers could use different underlay networks And we are seeing a lot of customers really look at configuring it in a high available A manner with with a fiber connection a coax connection And an lte is for backup So I think one of the things that's very important for investment protection is is two things one is You know partnering with the right network providers that can really provide that scale so they can take you from You know two megs up to 10 gigs, you know, depending on how you grow and exactly how big of a network You need to have how much speed you need to have Then also thinking about You know the difference between symmetrical And some of and some of the things that can be put in like even at over hsc and some of these types of technologies The other thing that I think is important is is to work with partners that give you a lot of Pricing flexibility or financial flexibility Meaning providing fully managed service so you can outsource some of the support But then also having no ets or early termination fees So you can you can trial stuff put it in five sites Make sure it's right for you and if it isn't and you can step away from it so that you're not locked into You know a contract for for that overlay Thank you bill ryan. I would like to ask you the same question Appreciate it and I add what I was saying was I think bill has really um hit on um the the flexibility and the scalability And I think in the world that we're in and and it's been sort of the theme throughout all of the comments that we've heard Things are changing at a pace that's pretty unbelievable in terms of the marketplace in general and how companies are approaching it So specifically when the companies are picking infrastructure What it really comes down to now is scalability And elasticity You know the the all of these questions are really driving towards the same thing Which is that organizations that I really need to take a look at their infrastructure From a standpoint of how quickly can we scale this up? How quickly can we build and and then what is the cost point for that? I mean bill was really talking about things like ETFs um and managing costs. I mean, uh, the reality is if you had endless budget and You know endless time you could do just about anything But for all the clients and for most of us work with the discussion always Realistically is um, how do we you know, and I hate to use the term But how do we future proof this and so the technologies that we're recommending today? um Really are designed to allow for that quick scalability whether it's on the cloud platform that somebody's looking at The orchestration of the automation tools that somebody's using. I know we're going to talk about that in a minute um, you know taking a look at The underlying network in terms of the actual connectivity whether they're using sd-wan whether they're using Flex type of solution. So those things are so critical because as these organizations are growing um And as the use of data as iot as all these things are starting to come more and more into play The flexibility and the elasticity the scalability is the most critical component for us in terms of starting to pick some of the infrastructure Um, and then what tools can you incorporate into that? As I said, you know, there's some tools that are really great They're really cost effective But they're very Dispoken limited in terms of what we can incorporate into that versus other tools that may have a little bit more service required up front But give an enormous amount of scalability in terms of where we can go And so we are really starting to take a look at technologies that allow for For a scale beyond what we thought was possible, you know, even three or four years ago Right, can we get your thoughts? sure I I recommend, uh, you know, of course solutions that are scalable future-proof secure And uh and use open architectures. Um, you know Examples include, you know standard edge models or even preset pre-staged edge centers cloud-based software management tools that connect the locations in the ecosystem During deployment and operations and and even open and and and very secure api So all partners can, you know, can access sort of fundamental, you know, fundamental capabilities and building blocks for efficient deployment and And operations and maintenance post deployment All right. Thank you Our next discussion point talks about automation and analytics So how can automation and analytics help simplify operations and resolve user impacting issues? Let's start with ryan No, great. Thank you. Um, so this is actually an area where where data canopy just believes that there's, um Almost blue ocean in terms of of the things that are going on in the space. So, um, you know, obviously as a as a cloud Um architect, we believe very heavily in automation and orchestration tools So, you know technologies like a kubernetes docker Leveraging microservices and sorry the bad locations Really refactoring and optimizing applications to work with the edge network To create efficiencies that potentially previously didn't exist and it's been talked about again a couple times on this call in terms of things like distributed network leveraging geographical Um, uh, efficiency and lease lease cost latency to To help clients and so when you really start to get into Taking a look at analytics taking a look at how we're interpreting the data How we're then turning that data into business case and using that data to design where You're going to build your next facility or where you're going to put your staff or any of those types of things We can actually start to use that data to do that and then leveraging that automation Whether it's containerization or some of the other technologies that we're using for faster deployment more cost effective deployments Leveraging microservices for better performance. So this particular area for us and I probably got a little more excited than I needed to for this but These types of technologies in the space that we're in are really what's starting to differentiate how Our client base can use cloud technology To improve their organizations and to better integrate with the edge which Before now has been a lot of very heavy lifting on the network side But we're really starting to see that marriage of uh, the application and and cloud to the edge in a way that's Much more seamless than it used to be All right. Thank you Ryan Frank Would you like to weigh in on this one? Sure. Yeah, um, I mean big data and and analytics Can can significantly speed network deployments and simplify Operations to really help resolve user impacting issues From a deployment perspective geospatial data From field personnel can streamline productivity Reduce paperwork costs and schedules at render we've seen Our network operator and construction partners use our geospatial technology big data and automation To reduce large-scale deployment schedules up to 50 percent percent From a maintenance perspective operators are using big data and machine learning analytics To more quickly isolate network outages or even detect potential performance issues Uh before they happen with with predictive analytics All right. Thank you frank dean What are your thoughts? Yes, thanks. Um, so I show some of the excitement in this area It's been interesting to watch over the years as The networks themselves the technology that powers a lot of these networks Has been somewhat opaque for quite a long time and just recently now we're starting to see You know from the ground up from the equipment on up the ability to see what's going on To get information out of the gear to get statistics and performance monitoring out of all different points in the network And whether you're on the enterprise kind of consumer side or on the service provider Supply side of this communications, you know, the ability to see what's going on is critical To see not only what's wrong and fix it But to proactively see what might go wrong You know, we've been we've been involved in this for a number of years have actually developed some software solutions We have a product And we've got case after case now of Users that are eliminating truck rolls or reducing truck rolls Really reducing mean time to repair by being able to see what's going on in the network And being able to see not only what's going on now, but what might be going on Three weeks three months from now based on performance statistics From the consumer side, we've been talking to a number of our enterprise customers That are really looking at these analytics to produce Measurable business gains looking at where application performance Their infrastructure is not supporting the applications in the way they need And that really does impact productivity business efficiency of their operations How do you streamline your network connectivity to give you better application performance and increase performance of your field personnel or your, you know, office personnel and how do you really Fully leverage the resources that you are buying So capacity planning types of things where you can limit your overall spend but yet increase business Capability all these things come out of those big data numbers come out of that Instrumentation of the network and be able to see what you're using what's working. What's not working tremendous tremendous area for increasing productivity and efficiency in this communication space. Yeah, we love it All right. Thank you Dean New trends in digitization and hybrid cloud have a direct impact on how networking and application security are implemented across environments What services enable secure workloads in any cloud environment? I'd like to start with Manish Thanks Laura. So I think I think first off, I think we should we should Look into how the physical layer of the network Interacts with the transport layer and the and the application. So At the at the base level, you need the physical layer, which is again, I come back to the infrastructure You need the infrastructure to deliver that that high level of of security and services that come into play So the physical layer has to have that high capacity fighter has to have the endpoints from a From a mobile network perspective enabled The the transport layer today is is extremely important because you've got to be able to connect to the data centers And in a secure environment So so you have to connect to the data centers and you have to connect between data centers um, you have to have a diversity burden so that the the uh, the The network is is never There's no single point of failure in the network Um, and then you have to have the application layer built in which is the connectivity to the cloud cloud So all of that has to work together. It has to be a dedicated You know flexible architecture like we talked about And in in that in that in that whole run you have to have the predictability of the of the of the services coming to play You have to make sure that the network can scale for the right network requirements and then It has to be secure. So it has to be highly encryption based so that you can you can do the you can you can transfer data In the most secure environment. So as we transition to this hybrid cloud In fact, as we have transitioned to the hybrid cloud this this This secure environment has become even more important And the underlying network that that takes this this this uh, provides you the connectivity Has to be you know both on secure end to end Hey, thank you. Manish Ryan. We're going to send it over to you Um, I uh, I I was saying I I couldn't agree more with what uh, with what manish was saying Um, I actually wrote down a few notes for this particular question and the number one thing that I talked about was uh, With security Because what we see and and you know data canopy we uh, like to say we work a lot with regulated or complicated companies, right? And the companies that we work with their healthcare financial services government, you know, those types of organizations Um, and so they're dealing with issues of latency They have very specific locations specific requirements So we work with organizations that are doing work in europe and asia and all over the globe That have specific local requirements in addition to their own internal policy Um, and you know, uh, if you're doing work in china You have a whole nother bag of issues to deal with it's a great firewall and so on and so forth So when we start to really talk about how you integrate a hybrid multi cloud approach and how you're actually managing workloads Um, it's probably for us from a security standpoint one of the most, um Um One of the biggest conversations that we're now having with our clients because it used to be really it was A more monolithic type of environment and as these services have started to get chopped up Push further out to the edge and then you have different Uh people in different locations accessing these services from all over the globe The complexity of that security and to um an issues point that includes everything at every single layer So, you know, the technology is that we're recommending now go all the way from your physical layer all the way up through the application layer where We're doing different services in different locations. Some services can't be in some locations. So When we talk about really managing workloads and in our multi cloud and our hybrid cloud environments We're doing it almost the location by location, but then you still have to have the the master Um kind of security policy as well. So that for us is probably the hardest and the number one conversation that we're having It's how do we really execute on a security strategy across? Uh a geospatial type of an environment Okay, thank you ryan. You do have a chance to redeem yourself on the mute button I think we have a few more comments and thoughts coming up for you in just a bit. So get ready And next we're going to go to dean dean I'd like to get your thoughts to round out the last thoughts on this discussion point Yeah, I I think munition ryan have covered a lot of it. Um, you know, we work with both providers and consumers on across a number of industries and they're now dealing with um a complex environment where The particular industry may have data at rest and now increasingly data and flight security requirements They need to be able to secure their communications Um, and at the same time their network is being more and more fragmented You know, we've talked about this move to the work at you know work from home kind of model You know, we're seeing the rise of you know, at first it was the branch kind of sd-wan model With remote branches running over or bring your own connectivity Now we're seeing this rise of the sassy kind of secure edge where it's almost down to an individual user Um, almost all the all the industries are working with are really moving toward almost a zero trust model Where you have to really secure almost every device every communication pathway It is the number one conversation we have with customers right after can you get me from a to b? It's okay, but now I just I can get there, but now it needs to be secure I need to be able to monitor it and I need to be able to rely on it These are these are the number one conversations we're having with people across the board And just as you know echo a comment I made earlier, you know that the criticality of network communications businesses can't rely on Handing paper from one desk to another they have to be able to communicate electronically or they just can't do business today It's becoming their lifeblood Hey, thank you very much. And this is our final Discussion point for this session. We do have a few audience questions that are coming in We're going to get to address those as many as we can during the time we have together So let's start with this last question here What next-gen infrastructure predictions can you offer? So this is going to go to the entire panel and just weighing in on your next-gen infrastructure predictions So let's start with Manish Thanks, Doran again So I think I think it's it's the prediction that I would make is we we as a As an industry are going to go back into the grassroots and in that trying to Again get back into the trenches and figure out, you know, what is the network architecture? you know really Require for the for the network of the future And the network of the future, you know, and today, I mean yesterday at a at a significant You know, I would say inflection point here Where is where what we are building today is going to define because we have the early early stages of 5g You know and in 5g as a technology Will transition, you know a lot of the the activities that we take, you know, not only in a personal life, but in a business life also, right? Um Where you get get back to is how do you build that that physical? You know the underlying network with with fibers small cells macros all working together How do you um get that edge infrastructure in place because the edge infrastructure Will be super important. You see different companies in our industry do different things with the edge, you know You have the tower companies bringing in the edge, you know at the tower space We are working at on on different, you know, uh bringing the edge even closer to the user from an in building perspective Okay, so we are looking at pico hubs. You're looking at Micro house you're looking at nano hubs and seeing how these hubs are going to be, you know Designed and deployed so that they can enable that edge, you know, you know, you need the edge intelligence You need the edge routing you need the edge Cashing and content distribution and so on that has to happen All of that requires the edge to be closer and closer to the user for that for that end user experience to happen And then and then everything has to then connect to the cloud So at some point right now what we are looking at is Getting back the grassroot and designing that network of the future and that's my prediction right now is Is 2021 will be about enabling this transition to the cloud But at the same time the cios and the and the and the visionaries are going to go back to the grassroots and look at How you truly design this this this network that can that can do the the Can enable the applications that would ride on 5g and the future g's that come into play I thank you manish bill. Let's turn it to you Yeah, I agree with a lot of what manesh said there I think the other thing that we're excited about is is doxus and where that leads us in terms of getting into doxus 4.0 and getting to 10 gigs at some point to keep those those wire connections I think the other two trends that that we're seeing is um, kind of the the use of software to find networking and and the virtualization of Hardware basically the branch office that a lot of customers are looking to simplify that experience and not have A box for the utm and a box for their wireless and a box for their firewall and a box for this and a box for that Let's convert that all the software. Let's make them vnfs Let's have a universal CPE that that's at that branch and let's be able to push policies and be able to centrally manage that Will be a will be a big trend The other thing I think that This work from home phase will continue, you know, we're going to see You know people continue to have that kind of a model which will drive some interesting Challenges I guess for security as well as for just having a good high speed, you know experience for for those people working from home so that You know, they'll have their residential connection for internet for the kids and their school work and their gaming and And the spouse doing their work, but then also dropping in a second connection And really having kind of a business class You know internet connection into the home to really drive The high performance that people will need, you know as you know work from home continues Thank you bill Dean let's hear from you Um, so I've got a couple big themes. I think that are that are pretty pretty broad based across the networks Both with symboli and demand side one is simplification We've seen, you know, the hyper scalers the web scale guys come in and be very disruptive over the past Probably 10 years now In driving the complexity out of the network driving down the cost per bit That kind of thing and part of their strategy was to drive down the complexity So we're seeing increasingly the the different network layers being collapsed the devices being collapsed So they're simpler to use. They're more transparent and along with that automation We we've talked about sdn a little bit. I think bill mentioned, you know the ability to actually manage these devices Programmatically so that now we don't need 10 people watching a network to make sure everything's running We let the network monitor itself and just alert somebody if there's a problem that needs physical intervention So this ability to simplify to automate and that's going to enable, you know, Manish talked a little bit about The iot and the the scale of the networks and the the the reach of telecommunications You know from from not just, you know, a guy sitting at a desk in an office But now it's to every streetlight and to every road sign that might be talking back to the network and providing information We're getting getting its instructions, you know, that that complexity that that vast increase increase in reach and scale Of the communications networks, you know, we need to simplify We need to automate it and then that's going to just unleash I think this iot wave of increase in scale Thank you dean frank. What are your predictions? okay, yeah, I by certainly expect an acceleration and the shift to edge computing not only due to technology and applications that we've talked about but also due to the the broadband demands caused by the Covid pandemic I mean, we're already seeing the impacts some some of which we see in everyday life like The video streaming companies, uh, you know downgrading default Video, uh, you know, you know video settings from hd to standard and and some maybe not so obvious things happening like wireless operators deploying, uh Micro edge, you know edge data centers that at the cell sites But i'm i see that increasing, uh over time The other thing is, uh, you know No matter which iot number of connected devices Forecast you see it's all in the billions. I've seen, you know You know nine, you know, grow to 50 billion over the next few years. It's all very high and we didn't we didn't talk much about, uh, the increased security risks caused by iot devices many of these devices lack Lack security In them or or are neglected when they're deployed in an enterprise outdated software or default credentials that That can be used as backdoors into corporate networks And it's a big concern of the enterprise So so even despite those risks, I still see the iot deployment to grow But I also see iot security solutions And practices will grow Um, and then finally, uh, well two two more things You know this this tremendous demand for broadband and video-centric applications will require, uh, you know Businesses and deployment teams to be more efficient do more with less and and sess based Automation tools and maintenance tools will enable that And uh, you know, also businesses Should should engage ecosystem partners Know what they know know what they don't know and engage, uh You know companies and and partners such as those on on this panel to help make it happen Thank you And ryan, let's get your thoughts Well, I'm unmuted a good start so but um Yeah, I um, I Agree with a lot of what was said here I think that where I see the future is that there there really won't be something that we think of as The edge anymore. I think that As iot as we see more devices connected in as people start to Really leverage the types of technologies that we've always historically talked about as business But now get more into end user and consumer and as people work from home and as there's more e-learning and All of the things that that we're seeing I think you're just going to see a massive increase in consumption a massive increase in data a massive increase in In everything and I I actually don't know that we can quantify it yet I think that we think of ourselves as big consumers of data And consumers of network and edge today But I I think this is really the first inning of a nine inning game I think you're going to see an acceleration of that as organizations become more decentralized Or as they start to leverage these technologies in a more efficient way to broaden their own wheat reach As the cost for a lot of this goes down You'll see more adoption in smaller companies which will increase competition With with all organizations So I don't think that we're seeing A small shift in the market I think that this is going to be seismic and I think that this is really The next evolution one thing that frank said that does have me concerned Is I do believe that we are also racing to catch up on security And so where I think the future is going to go is that We need to temper adoption of Some of these technologies with the need for the right types of security because there is Still a major concern in that space and I do agree with frank on that that it's moving at a pace that You know security always has trouble keeping up in general because of just the nature of technology, right? But what we're seeing now is that it's it's moving way too fast. So Um, so so that does give me a little bit of a restlessness at night But I know there's a lot of smart people out there including some of the people on this call that are working to To crack that now, but I I think we're just seeing the beginning of what is going to be a seismic shift in how Data is consumed used Analyzed and and how it affects our lives in all different ways business and personal Thank you so much ryan appreciate it and Unfortunately, that is all the time we have for our on-camera event our virtual event, but there's more to come hang on I do want to thank our expert panelists for a great discussion today informative insightful And definitely more conversations to be had on this topic. So thank you again Thank you And on behalf of Laura You're absolutely And on behalf of our panelists, I'd like to thank you everyone for tuning in and participating in today's round table Just a quick reminder our speakers are staying on for the remainder of the lunch hour to answer any more of your questions On linkedin and we did get quite a few questions come in Through our chat box. So thank you so much for sending those our way You will see our speakers over on linkedin. Just search Hashtag jsa virtual round tables or click the direct link in the chat box You can see it right there in your chat box to continue this q&a session And viewers if you are one of the first 100 registrants, we hope you enjoyed your lunch Make sure you visit us at jsa.net to register for more upcoming jsa virtual round tables Including our next one and last one for 2020 which takes place on december 10th Where leaders in our industry will talk about lessons learned from covet 19 and predictions for the new year ahead That is a wrap So look out for the playback of today's round table coming soon to jsa tv and jsa podcasts on youtube iTunes iHeart Spotify and more In the meantime, see you over on linkedin and happy networking Thank you


Now how much does acupuncture or seeing an alternative medicine doctor really cost? It's interesting because if you go to see a physician or you go into the American healthcare system without insurance, it can be literally outrageous the price you pay. I saw a recent study, a news article about a coronavirus patient who ended up leaving the hospital, thankfully alive, with a $1 million hospital bill.  But what does it cost to actually see an acupuncturist or a Chinese herbalist? Because that's what I'm talking about here all day long and you may be considering it now as an option. Let's jump into the video and discuss what it might cost to see an acupuncturist or a Chinese medicine practitioner. Hey, it's Dr. Alex Hine, author of the health book Master of the Day and also Chinese medicine doctor, internal medicine specialist and herbalist. So I've included two very important links below this video. The first link is to actually book to become a patient of mine in my private practice. So the first link below is not only going to have my email, it's going to have the direct scheduling link to become a patient or book an online telemedicine consult. Now the second link next to it is for a free download for subscribers and it's this Taoist monk named Li Qin Yun, who supposedly lived to be over 100 by doing these five practices every day. And in that PDF, I share what those are as well as a picture of this guy. So you can check them out right below this video. So the first thing that really dictates the price of going to see an acupuncturist or really any alternative medicine practitioner is what they're doing. So the modalities that they use and the modalities that they are practicing are going to be one of the biggest factors because again, you know, even to see a physician in America, the price is okay, you know, expensive, but not killer out of pocket. But as soon as you have an x-ray or a CT scan, because those machines are hundreds of thousands of dollars, if not millions of dollars, that can bring one visit up by three or $5,000. Same with surgery or having a titanium rod put into your hip, the intervention and modality affects the price. So for an average acupuncturist that's just doing acupuncture, the price is going to be very different from someone that does acupuncture, facial rejuvenation, cosmetic acupuncture, fertility-based acupuncture, post-stroke rehabilitation, or if they're an herbalist. So for example, myself as primarily an herbalist who does acupuncture with every session, every patient that comes in gets both acupuncture and they're going to get a formula for the week. And the value of the formula is number one, that it's basically like getting mini acupuncture treatments every single day. While I'm not seeing you, but for two, it often can really resolve some of that more deep-seated stuff that just, it takes time with chronic illness to actually resolve. So because of that, it takes, you know, there's a base visit fee, which for a lot of people ranges from $60 to $300, $500, as well as the return fee. And then for me, the fee of a patient taking herbs every week. On average, it's about $20 a week for me. Now, the second factor that dictates how much it's going to be to see a practitioner is where you live and basically the number of years of experience that the practitioner has. So for example, I was hanging out with a friend in New York City and he told me that he knows practitioners who have post-stroke rehabilitation clinics in Manhattan and upper and upper east side. And the visits could be over $500 to $600 per visit. I know practitioners who run fertility clinics and they run their practices just like an IVF in vitro fertilization clinic and they're $10,000 plus. So you have to pay the cost upfront and then if the patient does not get pregnant, they refund the remainder. So you have all the way from clinics that will charge you $10,000 for fertility, which could be the whole year just paid upfront or paid at a discount. And then you have people who are just charging high rates because that's an area of specialty. They deal with a certain clientele. It could be wealthier clientele. It could just be specialty conditions or their skill and it could just be the location. New York City being very, very expensive and Middle America, Kansas being not so expensive depending on the person, depending on where you are. So it varies quite a lot based on not only the modality, the way the person practices and also how often they want to see you. There are practitioners who they want you to book 12 to 24 treatments upfront, which is a third, a quarter, a half a year. And you have other people who are like, let me just see you for three visits, then I'll be able to give you a more proper and official cost because how could I possibly know how many visits it's gonna take you? You're a unique and different person and I don't want to book you into some sketchy package that you have to pay. So it varies wildly. So let's quickly take a look at some of the prices around the United States. I don't know where you may be in your country, but as far as the US goes, this is a pretty good estimate to help suss out pricing where and for what you're getting. I hope it helps you guys. That's just a ballpark figure. I would say the average figure is somewhere in between. It's probably between $70 and $120 return visit. And then if you're seeing me, the formula, which for me is the most important part of my clinical expertise, that's about $20 extra a week. So ideally, if you were to see me, it would be probably about one visit a week or one visit every two to three weeks, but you'd be taking a formula the whole time in between your visits. So maybe that helps you ballpark or budget or save because I know I've been in your situation as well. I saw practitioners for years and at the time, I needed the help and I didn't necessarily have quite enough money to do it, but I still did it anyway because resolving my health was the absolute priority for me, so I made it happen and for me it was completely worth it. And that's why I've decided to go into this field. So again, before you guys go, check out the two links below. The first is for booking an appointment with me as a patient in my private practice as well as my contact email down there below as well as the free guide Li Qingyun's five daily rituals to live to be over a hundred and his exact daily practices that he did. All right, before you go, don't forget to check out these two related videos here.


Hello, welcome back. In today's lectures, we will be looking at 2 important distributions. The first is the t-distribution and the next is the chi-squared distribution. Both these distributions are extensively applied in design of experiments. Before this, the most popular distribution we have studied is the normal distribution. The normal distribution had several desirable traits. By now we know that it is symmetric, mean, median and mode coincide and it is obeyed by many sampling distributions of the mean. Another nice thing about the normal distribution is that the parameters of the distribution mu and sigma coincide with the mean and standard deviation. We also were looking at the sampling distribution of the mean and we were looking at a large sample size and we also were considering the situation where the population parameter sigma namely the standard deviation was not known. So, hence it was recommended that we can substitute the sample statistic namely the standard deviation S instead of sigma. Using a large sample, the central limit theorem ensured that the distribution of the mean is normal, approximately normal in fact and we can substitute S for sigma. The natural question that arises is what will happen if I have a small sample size. In many practical situations, it may not be possible to have a large sample size. A large sample size had many desirable properties. It increased the precision while maintaining the level of confidence. It also enables non-normal populations to be considered in our analysis. However, we are now going to look at the case where the sample size is small and the population variance sigma is not known. The t-distribution sometimes also referred to as the students t-distribution is applied when the sample size n is small. How small is small is the query that immediately comes to us. Let us say that you have a small sample size of 6, 10 or 15. Only when the sample size exceeds 40, we can exploit the central limit theorem and also use S instead of sigma. But when the sample size is small, then we have to use the t-distribution. So, let us now look at the properties of the t-distribution. The important assumption made is that the population from which the sample was drawn is a normal population. In other words, the distribution of the population members is normal. This is a very important assumption. However, this is not a very binding or a very restrictive assumption in the sense that many of the populations behave close to normal type. So, this is not very serious assumption. So, small deviations from the normality for the parents probability distribution is permitted. However, what is to be done if the deviation from normality is quite significant, then we have to go for nonparametric tests. These are quite interesting but beyond the scope of our current discussion. The reason why we are doing the t-distribution and the chi-square distribution are, as I said earlier, they are extensively used in design of experiments methodologies and also when you look at any standard statistical analysis output, you will find the confidence intervals noted, the t values given. The chi-square distribution is the forerunner for the Fisher f-distribution that we will see in the next lecture. Let us now focus on the t-distribution. The t random variable is defined as shown in the next slide. This is quite similar, t is given by x bar – mu by s by root n. Well, you may think that I have seen something like this before. Indeed, we all have, we have seen the standard normal variable being defined as x bar – mu by sigma by root n. So, there is an important difference. z was given in terms of x bar – mu by sigma by root n whereas t is defined in terms of x bar – mu by s by root n. So, this is enough to create the difference between the normal distribution and the t-distribution. And the t-distribution also is not a universal distribution. We know that the normal distribution had parameters mu and sigma only. So, when you know mu and sigma, that pretty much described the normal distribution. Whereas, when you are looking at the t-distribution, we have the parameter mu and then we also have another parameter called as the degrees of freedom. When you normalize the random variable x by subtracting the population parameter from it and dividing it by s by root n, then the resulting random variable has a probability distribution which is centered at 0. This was the case also with the standard normal variable. However, the shape of the probability distribution for the t-random variable depends upon the sample size. So, when you have different sample sizes, the shape of the t-distribution also changes. Hence, the sample size is involved in the degrees of freedom. In fact, we say that this is the t-random variable which is following the t-distribution with n-1 degrees of freedom. Again, you might have seen this n-1 earlier. When you calculated the sample variance from the random sample data, you divided the square of the deviations by n-1. Hence, the same n-1 also figures as the degrees of freedom when describing the t-distribution. Well, we will not be really using the probability distribution function for the t-distribution. It is beyond the scope of the present scope and objectives to play around with the probability density function f of x. For completion, I am just giving the form of the t-distribution. It is gamma k plus 1 by 2 square root of pi k gamma k by 2 x square by k plus 1 to the power of k plus 1 by 2. So, what is this k? k is nothing but the degrees of freedom. Since the t-distribution is also having other applications, we do not use n-1 in terming the degrees of freedom. So, we use a general parameter k. But for our applications in statistics, we can set k is equal to n-1. But for general purposes, the parameter k is the degrees of freedom associated with the t-distribution. And another important thing is the mean and variance are not directly present in the t-distribution as they were present as parameters in the normal distribution. In fact, the mean and variance of the t-distribution are 0 and k by k minus 2 for k greater than 2 respectively. What it means is the mean is 0 and the variance is k by k minus 2. Of course, k cannot be equal to 2. So, the minimum degrees of freedom for the t-distribution would be greater than 2. It will be 3. Let us look at the t-distribution plots. Here they are. You can see that several graphs have been drawn here. And all these graphs are centered at the mean 0. The reason for that is we have centered the t-distribution at the origin. By making the transformation, t is equal to x bar-mu by s by root n. So, this is what we have done when defining the t-random variable. So, after you subtract by mu, the distribution gets centered at the origin. Mu is the mean of the population. It is the average value of the population. Please note that we do not know the value of mu. So, the question naturally arises is in order to define the t-random variable, you have the sample mean x bar. You have the sample standard deviation s and you have the sample size n. But you do not know mu. Then how will you have an value for the t-random variable? So, many of our statistical analysis in the future will involve testing of the means. So, we speculate or hypothesize on the value of the population mean mu. So, we are given an value of mu which is assumed or postulated or hypothesized or speculated and that value we can substitute here. So, we will see more on this in the future classes. So, now we are having different curves. Whereas, in the normal distribution, we had only one curve and a person looking at this curve cursorily or superficially will say, oh, this looks like a normal distribution. In fact, the t-distribution bears similarities with the normal distribution with the standard normal distribution because the mean is 0. The distribution is symmetric. 2 and – 2 are equidistant from the origin. So, if you go to 2, f of 2 will be equal to f of – 2. So, that is what is meant by the symmetric nature of the area enclosed by the curve is such that the area under the curve from 0 to let us say again 2 will be equal to the area enclosed by the curve when x varies from 0 to – 2. So, from 0 to – infinity, the area under the curve is 0.5. From 0 to plus infinity, the area under the curve is again 0.5. So, that the total area under the curve is equal to 1. That is the primary requirement of the probability distribution function. Now, where did these curves come from? These curves represent different values of k. One nice thing about the t-distribution is it remains symmetric even for low values of k. There are a few other distributions which we will see presently that are no longer symmetric when the k value or the degrees of freedom decrease. In this case, for k is equal to 3, you have this brown curve and then for k is equal to 7, you have the green curve. The blue curve is for k equals 11 and the dark brown curve for k is equal to 20. So, it can be seen that the curve becomes taller and the spread decreases when the degrees of freedom actually increases. If you can see this portion, I will highlight it. You can see the brown slightly above the dark brown curve. So, you cannot see much from this figure. So, let us go to the next figure which will make things clearer. So, the dashed brown curve corresponds to k is equal to 3. So, we are having a thicker tail for the t-distribution and when the k value increased, the curve became taller at the center but it became thinner at the tail. So, this is for k is equal to 20 and this is for k is equal to 3. So, you can see that when the degrees of freedom is less, then more probability is packed by the t-distribution in the tail portion. To summarize, as the k value increased, the distribution became tall and when the k value is small, the t-distribution became short at the center but it became thicker in the tail regions. These curves can be easily generated by a spreadsheet, okay. What you all have to do is to use the probability distribution and you see the x which is the independent variable here. You can take a very large value of x and a very small value of x. So, the range of x is from minus infinity to plus infinity. A small type was there. I will just correct it. It should be from minus infinity to plus infinity and k is the parameter. You can specify a value of k. You can say k is equal to 3, 4, whatever you want. Make sure the k value is specified to be greater than 2 and then you can define this function in spreadsheet, vary the value of x from let us say a very small number minus 20 and then go up to plus 20. The values of the probability distribution function f of x reduce t fast. You can see that even at k is equal to 3, if you go to minus 6 or plus 6, the value is pretty close to 0. And another thing you may notice is the curve changes its shape more and more slowly as the k value increases, okay. And beyond a certain value of k, a very high value of k, there would not be that much change in the shape of the curve. You can see that from k is equal to 3 to k is equal to 7, there is a big change. Whereas, from k is equal to 11 to k is equal to 20, the change is not much. So as I said earlier, the t distribution resembles the normal distribution with 0 mean and both are unimodal symmetric about the origin and have a maximum value at the origin. The t distribution is heavier in the tail portions and packs more probability in the tail region when compared to the normal distribution. Very interestingly, as k tends to infinity, the t distribution tends towards the normal distribution, okay. Many distributions share this attribute. In the extreme, the different distributions approach normality. k tending to infinity is a mathematical criterion, but when k exceeds let us say 40 or 50, it pretty much is close to the values given by the normal distribution. This degrees of freedom when we use with the t distribution also matches with the degrees of freedom associated with the sample standard deviation, yes. The degrees of freedom in the t distribution also matches with the degrees of freedom with the sample standard deviation. Whenever we use the sampling distribution of the mean for small samples, we have to use both the sample mean x bar and the sample standard deviation, yes. And the sample standard deviations associated with n-1 degrees of freedom, the reason for this we saw earlier in our discussions on the random variable and exploratory data analysis. We have n-1 degrees of freedom for the sample variance. The reason for that is not all the n deviations about the sample mean are independent. Only n-1 of them are independent. So, the sample standard deviation or the sample variance is based on n-1 degrees of freedom. When we use the t distribution, we also have k degrees of freedom. When we use the t distribution for the sampling distribution of the means, we use yes in the definition of the t random variable. We use yes in the definition of the t random variable. So, k becomes equal to n-1, where n is the sample size. So, whenever we use the t distribution for the sampling distribution of the mean calculations for small sample sizes, we use n-1 as the degrees of freedom for the calculation of probability values. Now where are these distributions used? In many practical situations, we have to see the probability of a random variable following between 2 values or being less than a particular value or being greater than a particular value. So, we have to find the probability. All the time, we cannot use the normal distribution. It depends on what distribution the random variable is following. What distribution? The random variable of our interest is following. Now when we talk about the distribution of the sample mean x bar for the case where the population parameter sigma is not known. For the case where the sample size n is small and for the case where the parent population is following the normal distribution, then we have to use the t probability distribution. So, whenever we are considering the probabilities of x bar lying between 2 values or greater than a particular value or less than a particular value, we have to use the t distribution. The probabilities have to be calculated using the t distribution. So, how do we get the probability values? So, if z alpha is a calculated value of the standard normal variable, we know that the probability of the standard normal random variable less than z alpha is equal to 1-alpha. So that the area beyond z alpha was alpha. So, this is what we used in the case of a normal distribution. Now, we define t alpha k such that for the specified k degrees of freedom, the area above this value in the t distribution curve is alpha. So, now we are having t alpha and k. k is the degrees of freedom. Let alpha be a specified value. We have seen earlier that in the generation of the 95% confidence intervals, the alpha value was given as 0.05. It may take values like 0.01 and 0.1 and so on but alpha is equal to 0.05 was quite frequent or usual. Now, suppose we have the same alpha. So, what is the probability of the random variable t taking a value greater than t alpha k? What is the probability that the t random variable takes a value greater than t alpha k? And we define alpha in such a way that probability of t greater than t of alpha k is equal to alpha. So, we define the subscript alpha in such a way that the t random variable exceeding t alpha k will take a probability of alpha. So, just note this definition. We will be looking at the t distribution curve to understand this further. So, t alpha k is an upper tail 100 alpha percentage point of the t distribution with k degrees of freedom. This statistical terminology is fascinating and also important. It is like grammar. We have to use the correct terminology. So, again I repeat t alpha k which is used in the probability calculation. It is usually a value okay. It is represented in a general term t alpha k here. It is a numerical value in fact. So, t alpha k is an upper tail 100 alpha percentage point of the t distribution with k degrees of freedom. What it means is whenever we are calculating the probability, once the value of alpha is specified, we look for the area under the curve beyond t alpha okay. In the cumulative normal distribution probability chart involving the standard normal variable, whenever a particular z value was specified, the probability tables gave the area under the curve below the value of z alpha okay. But in the t distribution, we are talking about the upper tail. So, whenever the value of alpha is specified, we are looking at the probability in the tail region beyond the value of t alpha and the area under the curve beyond the value of t alpha is alpha itself. So, we can say that the area of the distribution or the area covered by the distribution below the value of t alpha would be equal to 1-alpha. The total area under the curve is 1. The total area under the curve for any probability distribution by default by definition is equal to 1. So, summarizing probability of the t random variable with a specified degree of freedom k, taking on a value greater than t alpha, k is equal to alpha. So, this is the definition. Now, since the t distribution is symmetric about the origin, it may be easily shown that probability of t less than t 1-alpha k is equal to alpha as well. We are exploiting the symmetry of the distribution about the origin. So, if you locate a point t 1-alpha k on the x axis of the t distribution, the area below t 1-alpha k will be also equal to alpha. Now, it may be also seen that t 1-alpha k is equal to minus t alpha k because the t distribution is centered around the origin. So, one half of it corresponds to negative x axis values and the remaining half of it corresponds to positive x axis values. So, let us see how t 1-alpha k is equal to minus t alpha k. So, let us now look at this diagram. This is the t distribution for a specified degrees of freedom. The specified degrees of freedom k is equal to 3. This curve again may be generated using a spreadsheet. Now, let us fix the t alpha k which is a number at close to 2. Let me even make it at 2. Well, there is slight discrepancy but let us assume that t alpha k is equal to 2. So, the upper tail probability will be alpha because this is some chosen value of alpha and so the area covered by the upper tail is alpha. Now, if you want the lower tail probability also to be alpha then you should locate t 1-alpha k. The reason is the moment you put t 1-alpha here the upper tail is going to be 1-alpha. If the upper tail is 1-alpha then the lower tail value would be alpha. What is the relation between t 1-alpha k and t alpha k? Since t 1-alpha k is located on this side on the left hand side of the t distribution it would be a negative value but due to the symmetry of the t distribution t 1-alpha k will be located at a certain distance from the origin and that distance will be same as the distance of t alpha k from the origin. So, we can say that t alpha k is equal to minus of t 1-alpha k. So, this is the important relationship here. We can also say t 1-alpha k is equal to minus of t alpha k. So, this follows from the graph. Now, let us look at a typical probability chart for the t distribution probability table if you want to term it that way. So, the degrees of freedom are given here and the probability value is specified here. It is slightly different from the standard normal distribution. So, we have different probability values 0.4, 0.25, 0.1, 0.05, 0.025 so on to 0.0005. So, these probabilities are all upper tail values and the t value corresponding to this probability is given in these columns. So, the t value with a distribution for 4 degrees of freedom packing an upper tail value of 0.05 is 2.353. For 3 degrees of freedom it is 2.353 and the t value for 4 degrees of freedom is 2.132. So, if my degrees of freedom for a given application is 4 and I want to find the t value that will have a probability in the upper tail as 0.05 then the required t value is 2.132. So, as a degrees of freedom changes the probability is fixed but the t values will change. So, for a given probability as the degrees of freedom change the t values also change. What is interesting to note here is for packing a specific probability in the tail portion the value of t decreases as the degrees of freedom increases. What it means is as the degrees of freedom increases the tail becomes thin and when the tail becomes thin you have to go closer to the origin to pack more area. So, for a given probability the t value decreases with increasing degrees of freedom. It is very interesting to relate the figure with the data given in the table. By now you should know what is the z value corresponding to a probability of 0.05. In the cumulative distribution we talk about probability of 0.95 in the lower tail. In the t distribution we talk about the probability of 0.05 in the upper tail. Let us see what happens to the t value when the degrees of freedom increases. So, we are now looking at 0.05 and it is coming to 1.697 at 30 and at 600 it is 1.660 it is at 40 it is at 1.68 at 600 it is 1.66. So, the change is not much and at infinity we are having 1.645 1.645 is a very popular number and so there is not much difference between the t value and the z value because the z value is the standard normal distribution variable value. So, corresponding to a upper tail probability of 0.05 or a lower tail probability of 0.95 the z value is 1.645 and the t value for a very large number of degrees of freedom is 1.660. So, we can see that the t distribution tends towards the normal distribution with increasing degrees of freedom. Another famous probability is 0.025. So, you are talking usually about the 95% confidence level and since you are talking about upper tail and the lower tail we have a probability of 0.025 in the right hand side of the tail and 0.025 in the left hand side of the tail. So, the z value corresponding to 0.975 cumulative probability in the lower tail or 0.025 in the upper tail would be 1.96. So, for the standard normal variable we have 1.96. For a t distribution with an upper tail probability of 0.025 the degrees of freedom being 600 is 1.984. So, for the t distribution with 600 degrees of freedom the upper tail probability of 0.025 will correspond to a t value of 1.984. So, we can also generate confidence intervals for the t distribution. We are taking the small sample size. For the normal distribution we defined the confidence interval in this fashion. We were interested in obtaining the lower bound and the upper bound of the standardized random sample mean such that the probability value was 1-alpha. So, we were interested in finding out the lower bound-zalpha by 2 and the upper bound-zalpha by 2 such that the probability of-zalpha by 2 less than x bar-mu by sigma by root n less than zalpha by 2 was 1-alpha. Now we are taking a random sample from a normal distribution but the catch is the sample variance is not known. So, we are using the s value earlier. What do we do for the construction of the confidence interval? So, not surprisingly we use again the sample standard deviation s in constructing the confidence interval for the t distribution. So, we have probability of-talpha by 2 less than or equal to x bar-mu by s by root n less than or equal to talpha by 2 equals 1-alpha. The question is how do I find-talpha by 2 and plus talpha by 2 such that the probability of the standardized t random variable x bar-mu by s by root n lying between these 2 bounds will have a probability of 1-alpha. So, the t random variable we know is defined as x bar-mu by s by root n. So, we are having minus talpha by 2 n-1 and talpha by 2 n-1 here and you also may recall that minus talpha by 2 for n-1 degrees of freedom is nothing but t1-alpha by 2 n-1 because of the symmetric properties of the t distribution because of the symmetry properties of the t distribution. So, this is the basic definition for constructing the confidence interval. We can manipulate on either side of the inequalities to eventually get probability of x bar-talpha by 2 n-1 s by root n less than or equal to mu less than or equal to x bar plus talpha by 2 n-1 s by root n. Please note the use of capital S and capital X in the representation of the sample standard deviation and the sample mean respectively. And so, this is what we have from this equation we can write the confidence interval for the population mean as x bar-talpha by 2 n-1 into s by root n less than or equal to mu less than or equal to x bar plus talpha by 2 n-1 s by root n. So, you are having a small sample the sample is taken from a normal distribution from an assumed normal distribution and then we not only want a point estimate we also want an interval estimate and for constructing the interval estimate we define the t random variable. The t random variable in turn is defined in terms of the sample standard deviation s because the population standard deviation is not known. So, we have to define t as x bar-mu by s by root n and the degrees of freedom for the t distribution matches with the degrees of freedom used in the calculation of the sample standard deviation. So, once these are known we can easily construct the confidence interval and the confidence interval is given by this expression. So, this is referred to as the 100 into 1-alpha percentage confidence interval for the population mean mu. This is very important t alpha by 2 n-1 is referred to as the upper alpha by 2 into 100 percentage points of the t distribution with n-1 degrees of freedom. So, there is a typo I will just correct it should be percentage point not points it is a single point. So, this completes our discussion on the t distribution we use it for small samples the parent population is normal and the parent standard deviation sigma is not known parent population standard deviation sigma is not known we will continue shortly.


Here we are zooming into HEN 1357, known as the Stingray Nebula. Even though the universe is constantly changing, most processes are too slow to be observed within a human lifespan. However, this nebula is now providing scientists a unique opportunity to observe a system's evolution in real time. Stingray is the youngest known planetary nebula, having formed around the collapsing central supergiant star, HE3-1357, starting in 1987. By 1995, the central star was a white dwarf. Images captured by Hubble in 2016, when compared to Hubble images taken in 1996, show a nebula that has drastically dimmed in brightness and changed shape. White blue shells of gas near the center of the nebula have all but disappeared, and the wavy edges that earned this nebula its aquatic-themed name are virtually gone. The young nebula no longer shines as brightly against the black background of the distant universe. The oxygen gas emission, in particular, has dropped in brightness by a factor of nearly 1,000.