doesn't work. Okay, let's do it here. Okay, so good morning. My name is Laura Ferranti and I'm working at ECMWS and I'm working more on the sort of the operational side of the activity of ECMWS, so looking in the forecast department, so looking more really at the evaluation of the forecast. So I would like to give you today a sort of point of view of how we evaluate extend-range forecasts and try and try to assess their skill with particular attention to the ability of this forecast to simulate, represent the tropical and intertropical, tropical and estratropical interaction. So I would like to introduce really the concept of conditional skill in the extend-range forecast, the long-range forecast. We have, we know that some sources of predictability from which we justify to do extend-range forecasts and so when these sources are active, the skill is higher, when these sources are inactive, this skill is less announced. And here is really how my sort of responsibility in our team is to work and try to diagnose and improve the forecast on representing and exploit at a more effective way such a source of predictability. So ECMWS issues forecast at medium, subsistional and seasonal ranges. And if you look at the subsistional ranges, we are looking, we're trying to do prediction of events that don't represent the day-to-day variability but represent variability on the order of, let's say, week, week or five days. So events that tend to persist for about five days. And these such events are cold and warm spell or blocking events. And the source of predictability that is associated to this kind of forecast are based on the effect of the MGO, which we have heard many times during this week. And also other sources of predictability on the stand scale come from the land surface condition, the cryosphere, and the stratospheric southern warming. For the seasonal forecast, we are trying to predict and so, the variability on and so, and therefore we are trying to predict anomalies that tend to persist for longer time, typically months or seasons. And again, this kind of long range forecast relies on the source of predictability such as ENSO, global climate change, decade of variability, land surface cryosphere, and interaction with the stratosphere. So because here we are talking about tropical interaction, we focus on the MGO for the subsistional time and the ENSO on the seasonal time, but we should not forget that we are also looking at other sources. So the idea here is really the conditional scale. So we know, for example, if you look at the seasonal forecast, that if we stratify the scale of taking ENSO here or taking the whole sample, we have a different value of scale. So this is a paper from Melissa and Simo Payeva in 2008, but actually did exactly that. So they look at the scale for a three-month average over US, which are temperature forecast, and you have the scale in terms of the function of the lead month, the time, and then you see that they have actually put all the samples together, and you have the scale that is defined by the diamond somewhere in the middle of the three curves, and then if you actually state it, just say to the ENSO happy source, you have a much higher scale. So this is the concept of the sort of conditional scale, looking at the opportunity given by the ENSO. So you can do the same for the subsistional time scale, and this is actually a bit of an historical thing, because at the beginning the subsistional was something that was not actually thought that was possible, because the MGO, which is the most important mode of intracellular variability in the tropics, was actually very well defined and detected, only in the 1970s. And so at the beginning, when there was a numerical weather prediction, we were seriously focusing to improve the forecast on the extra topic, and there was this idea that the tropical didn't really matter very much. But then with the knowledge of the existence of the MGO and the importance of the interaction between tropics and extra tropics, it became clear that the idea that although the mid-latid variability is really driven by the internal dynamics, there is an important part of the tropics role that can modulate such variability. So we can have predictability in a time scale, or in a subsistional time scale. So this again is another old paper from Alejandro Natale in 2000, where we are trying to look at the same thing. So let's say, what about if we look at the skill stratified by looking at an event where there is an MGO on an event where there is not an MGO? And actually, this is a skill measure in terms of anomaly correlation over the extra tropics, so there's another MGO. And this is funny that they got exactly the opposite of what we are saying here. So they got a higher skill for the event where there was no MGO, and they got a lower skill for the event where there was an MGO. And you wonder why? And the reason why is actually that the focus at that time, they were not very good. So it was very difficult actually to represent MGO events. And so we had to put quite a bit of effort to represent the tropical variability right to get the predictability associated with the MGO. So at that time, this was the sort of the statement that was coming out from this paper. So less skill for forecast with MGO events is actually due to the inability of the model at that time to sustain the MGO. And therefore, there was no rugby way source that was creating this interconnection into the extra tropics. So there was several papers that at that point state the importance of using the other in the tropics, the importance of representing the MGO correctly. And in this way, to be able to exploit really the response in the extra tropics. So importance of reproducing the teleconnection for the focus field on the subsistional time scale. So after that, lots of work has been done to try to reproduce, to try to make models more accurate in reproducing the MGO. And so even producing the variability in the tropics in the right, more accurate as possible. And at this MWF, we measure very careful the kind of progress we do in representing the MGO event. And this is a paper from Frederick Vita in 2012, which by using a re-forecast has actually created a sort of the evolution of the skill of the MGO. So how a system progress every year we do, we apply, we implement roughly two cycles per year in which we include, include the modification and progress in representing the physical representations, we announce resolution, horizontal, and spatial, and so on. And so this is basically the evolution of the skill of the MGO as a function of the from 2002 where we started to do the subsistional process. So this red line is basically the anomaly code is the days, the skill is as a function is the time in the years, the evolution in time, and on the Y axis is the number of days, the days. So it's basically how, when, it's when the skill, which day the skill goes under 0.5, this is the anomaly correlation. And so you can see that we have actually gained quite a bit of number of days from 2002 to 2013. Associated with that, there is a sort of correspondence in looking at a similar evolution of the skill, but this time looking at the parameter in the northern hemisphere, so this is the standard. So you have an evolution. So that's where we believe is the foundation of working on the subsistional time scale. So I guess if you have already seen these pictures, I'm going quite quickly on that. So one of the, the work we are, one of the points we are trying to do then is not only assessing how much the skill, how the skill is modulated by the different source of predictability. So we are looking at conditional skills, but also trying to understand how the teleconnection in the model are reproduced. This is goes back also to all the work that Franco does. And this is an example from again in which using the SOS data set, look at the teleconnections associated with the MGO. So these are composites of geopotential height, 11-15 days left with respect to MGO events that are invasive, so there is an active phase over the Indian Ocean. And you can see the response are quite, there is a quite different phase of the response, which as a reference should be the one on top, which is the response from the era in the ring. So it's now a source of reference verification response. And it's again the MGO structure that we are looking at after. What are these numbers? These numbers are believed to be the correlation for, it's a correlation to an MGO standard pattern, just to give a sort of report if I measure what flow is. So as I said, we don't look only at, so when we do this skill, a conditional skill, we don't look only at the probabilist or topical interaction. We try to really look at all the impacts, all the sorts of stability. And in this case, this is a work from C.C.I.D.D.A.L.D. in which it actually stratifies the skill as a function of whether you have or not the stratocerics of the world. So in this case here we are looking at the condition that's still associated with the stratosphere. And you can see that for the event, this is a function different week, week one, two, and three. And this is still for two weeks of tension over two different regions, Russia and Canada. And you see that the red bar represents still for events with the stratocerics of the world and the blue without. So you see that there is an effect. So this is one of the work typically we are doing. But today I would like to talk a bit more of trying to ask, at the moment we are focused on our effort in trying to ask the questions of this tool. Can we predict weeks ahead, the changes in large-scale flow? And in particular we are interested here at predicting in advance cold spell over Europe. The idea is that cold and also warm spell in summer, they actually, they have a strong impact in society. This is an example for February 2012 where the water of Daniels were completely frozen. And so the idea is really, can we use, can we make a good use of subsistence of forecast for the society? So we have been looking at this for quite some times. And for example, we have been looking at the ability of the subsistence forecast in predicting the summer 2003. And I've been looking more generally at the ability of the forecast in predicting heat waves. And we had this impression that really the important thing is to get the transition to an anti-cyclonic flow regime right. So because both east and cold waves, they're really associated to an anti-cyclonic circulation that persists for some time. And so we are really focused really on the ability of predicting this special flow circulation that facilitates this high-impact weather. So for this we are looking at, we are trying to look at weather regimes and stuff like this. And these are the weather regimes. I think we have been looking at weather regimes quite a bit. So I'm not going to describe them. We have these four weather regimes which have been founded by many people. Franco has given a very thorough overview about this concept and the theory on it. So I'm not going to make too much comment about it. But I would just say the reasons why we're looking at this. So we're looking at these four regimes because they are associated with the high-impact events, particularly the blocking over Greenland, which is also called the negative state of the LAO, and the seminarian blocking. We have two final regimes which are certainly associated with persistent anomalies of temperature, which can be defined as a high-temperature event. We are looking at them because they are typically quite long life cycles. They tend to persist longer than a week. So they are really a typical object that can be focused in this seasonal timescale. And also because they are associated through erotic waves, they are associated with Indian in the tropics. So we have all the ingredients to be the right target for the substance of forecast. So here I show you sort of the skill of these four regimes starting in terms of anomaly correlation from the function of day from day 3 to day 30. The skill has been filtered with a running mean. And I've actually picked up, this is a based, it's a quite robust measure of the skill, because it's based on reforcelment to S, and I've picked up a number of models available on S to S. And you can see that there is some potential there. We have quite a distant skill that goes well beyond 10 days for these four regimes. There is quite a bit of range of variability among the models, but the last one is the European Central. So I think it's encouraging this kind of result. Yeah. This is anomaly. I mean, I show this, but I could show you also we have done a lot of also skill, probabilistic skills of the forecast. It gives very similar results. Yeah. The question here is that going back to the fact that, okay, the fact that you, we have a decent skill on predicting these regimes is important, but we are really interesting on understanding whether we can say something on the transition from one regime to another on the onset of this heat or cold spell. And this is a much more difficult kind of questions. And trying to address this, we have sort of created a very, very simple framework. So we are now going into two dimensional world defined by two, the first two leading UF in geopotential height. So if you calculate the first two UF in the geopotential height, you can find that the first one typically is NNEO pattern. And the second one is the kind of Scandinavian blocking, if you like. Now, this is very simple, very symmetric. And these two UF is playing together just 30% of the winter variable. So it's a very, very simplified and very limited kind of framework. But we wanted really to understand the transitions and, you know, if you are in two dimensional space, this is possible. So here is an example of our space. So here we have the UF1, and here we have the UF2. And basically, if you are familiar with the MGO index from Hendon and Wheeler, this is exactly the analogy of that index in the isotropics. So to show you if it works, we have actually projected the daily fields of two winters, two extreme winters in the North Atlantic sector. The winter 13, 14, which was a winter that was very stormy and with mild temperature. And it was actually projected most of the time into an annual positive. So we experienced that winter very strong, westerly going across Atlantic. And you can see this is a, you can actually follow the evolutions of the anomaly of this, of this winter, the daily evolution from December, January, February, this color coded looking at this diagram. And on the other side, you see the winter 2009, 2010, where instead it was a rather contrasting winter, because it was a winter in which most of the time we had a kind of a grill and blocking. So just an opposite condition. So very, very cold condition of Northern Europe. And you can see there that there was quite going between blocking and the annual negative. So it seems like that the list for these two particularly contrasting winter, the description in this very simple framework is effective. These are the two mid-attempt, two mid-attempture anomaly for the, for all the winter seasonal anomaly for 2013 and 14 and 2009 to show you the relation with the temperature. So we started to use this device for the forecaster. So now the forecaster are actually taking this kind of information here and they make quite a big use. They have grown very fond of these things. And so now here what we are looking at, example of operation of forecast. This is a medium range forecast. So these are two different forecasts. This is initiated the 3rd of May. The other one is initiated the 15th, 25th of April. And you can see if you start with this one, this is the analysis that comes before the forecast. This is the initial condition of the forecast. So it's time zero. And this is after one day, after two days, and so on. And so you can see that the cloud of the members, we are looking at 51 members here, become bigger and bigger when you go further in the forecast. And here you see the transition is going. And this is another forecast for the other case. So looking at this is very easy visually where we are going. And the forecaster seems to have quite passionate about it. It's available for member states at the moment as a testing product. But next year we are trying to make it available. Sorry? Member states. Yeah, is the MWF as a member? No, no, no, no, American. Sorry. So this actually, you can actually do, we can also do it. This is even more sort of on a research side. We can also apply this for forecaster that reach up to 46 days. In this case, this is an example of a forecast initiates on the 27th of April, which start here somewhere here. And then now we are looking, because this is an extended range forecast, we are looking every five days. So this is day zero. And the blue is day five. The light blue is day 10. And you can see how the clouds open up. Now I have to apologize. The graphic is not ideal here. Should have been smooth out to making different colors and so on. But you can appreciate that even at this range by day 15 to 20, you can actually see that the forecast is doing a very big evolution into this phase space. Actually, this is the verifying analysis. So I plotted a posteriority for this sake. And in fact, this forecast actually gave an anomaly of cold, because here we are going into negative temperature here. So there is a strong relation with the forecasting temperature, which was verified. So of course, this is a successful story is one particular forecast. It doesn't mean that we get it right all the time. But we went to see why this forecast was good. And the reason why this forecast was good is because we had an MGO. And this is quite impressive. So we had an MGO traveling around. And we believe so these are two MGO forecasts for a similar period that give you really the hint of how these two are connected. And we always, when we're trying to train a forecast to use our forecast in the substantial time scale, we always say, even if you make your outlook of Europe look at the MGO, it's very important. Because if you look at the MGO, you can have confidence to your forecast. So going back now, this was one case. Now we want to look at the evaluate the skill more in a general way. So we look again at the reef workers now, and we look at the anomaly correlation for UF1 and UF2 separately. And we can see that these are all the same different models for S2S taken from S2S. And you have the UF1 is the pattern that represents the NEO variability, the symmetric part of the NEO variability. And the UF2 is the pattern that represents the blocking. So you can see that the blocking, the predictability of the blocking, the skill is a bit of a shorter time, drop up to about 14 days. The NEO is a bit longer. But then again, stealing the ideas from the MGO guys that they have come out with a bivariate correlation. You can also do the bivariate correlation for the UF1 and UF2. And this gives us really the skill of really how good we are in performing the evolution in these two dimensional phase space. And again, so it gives us some hope that we can do, we can get some prediction of cold spell or warm spell beyond the medium range. So we can also go back now to the nice talk that Angel has given some days ago about how we can look at frequency transition. And this is exactly one of your diagram. I thought, oh, he has told them my word. So this is one of the diagram that you are doing as well. We have applied the same diagram, but in the two dimensional phase space. So here what you are looking at is trying to understand how the evolution in this very simple framework works. How is the typical, the preferred transitions. So what we have been looking at is the frequency of the transition going into blocking. So for example, if you fix it into this part of the diagram. So here I have counted the, I'm looking at about 36 years, the daily data of error in looking into transition into blocking. And so this is the column with a sort of a solid line, represent the analysis, the verification and tell you what is the percentage of frequency in which if you end up in a blocking, you are eight days, between eight and six days, you were already in the blocking. So give you the frequency of transition for persistence. So this is the persistence contribution. And this is the contribution coming from any opacity, for any negative and for getting sort of no blocking or Atlantic reach. So you can see that when the colors more or less correspond. And this is done also for different focus ranges. So if this diagram I would have shown, because we have done a different focus range, you can appreciate whether in the focus there is a bias. So if the focus is actually has a problem to reproduce this transition, you would have a very sort of inconsistent colors here in this part. But we don't find much of this. Actually we find that it's quite, I'm looking at the different ranges from 11, 16, 21 up to 30 days. And you can see that the focus actually is quite able to reproduce quite accurately the transitions divided into the different colors. I think what is extremely interesting is this part of the diagram where you're looking at transition into the annual. So this is going in this diagram going on this direction. I put to that very thick arrow, because this is a very strong statistics. So it tells you that basically most of the days that go, most of the situation in which you go into a negative is they are coming from blocking. So it's really a typical, the typical evolution into a Greenland block is a block, a Scandinavian block. And then you can study as much as you like. But I think this is really, again, is an important fact, the fact that you have to check whether we have strong biases in the model. So then you can go back and you apply again this idea of the conditional skill into the MGO, because we have seen that there are cases with the MGO. And we know also that the frequency of the NEO is connected with the MGO activity. And this is basically the Bavarian correlation between UF1 and UF2 for cases with MGO and without MGO. This is only our own forecast, because otherwise it would be too many curves to understand. And you can see that there is definitely an improvement when it's better. We have a higher skill in making, following this evolution in this two-dimensional phase space for cases where we have an MGO that is active. Then you can also, I'm also finished, when we're finished. You can also split and going to look at the symmetry between NEO positive and NEO negative. And this is what we have been doing here. Now we are looking at the skill in terms of a probabilistic measure. These are the Bavarian skills course, which measure the mean square error in probability space. And it's a skills course, which means that if you go up to 1, you have a transfer model. If you go to 0, the climatological forecast is better than your forecast. So you want to be above 0. And again, these are the skill with and without MGO. The skill with MGO is the red line, without is the black line. And then the sort of almost parallel curve over there, parallel to the x axis is actually the resolution. The reliability skills course, which gives you a measure of how the probability of the forecast match with the frequency of occurrence of the event. And so you can see that the difference between these two curves is not very large. And in fact, it is not even significant. So what the statement we can say here is that for the NEO positive prediction, the skill sensitivity to MGO is small and not significant. But when you look actually, you do the same things for the negative NEO, you actually find a quite significant skill. And this is quite impressive actually. And it has a skill in the Brazky's course and also in the reliability component. So the forecast is significantly more reliable. So at the beginning I was scratching my head and I thought, why we have such a symmetry? But this actually seems to be fit very well with the recent work that Helene has done, which shows that there is an asymmetry actually in the interconnection between NEO positive and NEO negative. And the interconnection with the NEO negative are much stronger. It seems to fit with these results. And so I think here is the summary. So forecast scale as subsistional and seasonal range is conditioned by the main modes of tropical variability and so on MGO. So when we assess the model, we need to make sure that the variability of these important modes is very well represented. And also we need to make sure that forecast subsistional and seasonal scale are quite accurate in reproduced teleconnections. Then just say words that the SOS archive is extremely valuable tool to assess predictability. I'll show you a bit the potential of these two-dimensional diagram which is very simple, very limited, but it has quite, it facilitates understanding transitions among some important flow patterns. I'll show you that we have this asymmetry. We have found this asymmetry in the skills course sensitivity with MGO. So where we found the most highest sensitivity for the NEO negative and not significant sensitivity for NEO positive.


Well, first of all, thanks for coming to this panel. I was realizing before, I think, this might be the first in-person presenting experience, so hopefully we'll not have any nerves, but definitely with a smaller group. We have plenty of stuff to present, but hopefully it also can be moments to pause for conversation and questions as we go. So I will quickly kick us off. So first of all, actually, the topic, just to make sure y'all are in the right place, obviously, we're here to talk about continuous optimization and consensus building and approach to web and platform work, and so we'll do a quick intro of ourselves. I'll start off. I'm Katie Jamison. I am a senior VP at Blue State, and I'm gonna hand it over to Taylor for quick intro, and we'll talk about where we work. Hi, everyone. My name is Taylor Darnell. I'm a senior website and marketing manager at MSFUSA. I'm probably not the only one whose haircut has changed dramatically over the last two years, but we are here to talk about a different sort of change management, and I did plan that joke two days ago. So what is MSF? Well, it's an international organization that provides critical medical humanitarian aid around the world wherever it's needed most, whether it is epidemics, pandemics, conflict zones, natural disasters. What we're trying to do as an organization, obviously, is save lives, and are often the first people into really dire situations to provide that care. We want to stress always that it's independent, impartial, something that is independently funded, doesn't operate based on the mandates or approvals of governments and governing bodies. Yeah, and it's been around for 50 years if I hadn't mentioned since 1971, and I'll get into a little bit later, kind of the specifics of what we're talking about when it comes to the web property, doctorswithoutborders.org, there is kind of a different relationship or it's not as direct as, you know, we worked on a site for all of MSF, but I'll get into that in a second. And I work for Blue State. So I have a colleague of ours over here, Sam. We presented in the same room a few days ago. Blue State is a digital agency. We do work primarily in the nonprofit and advocacy sectors. And we'll talk about this in a second. We've worked with MSF for many, many years, and Blue State is an affirm that basically does work across the spectrum, including web platform design, but then also runs full service campaigns, spanning email, social for a number of nonprofits for fundraising, advocacy, and brand engagement. So we have a pretty strong and robust digital platform practice, which is actually led up by my colleague Sam over here in the front. But we also have a unique POV where we're not just looking at that channel alone, we're really looking at the full suite of things, which I think is a good segue to some of the ways that we've approached thinking about work in partnership with MSF. So I'll kick us off. So just in terms of, you know, the topic at hand, you know, part of what we're really wanting to talk about in this is, you know, a lot of the panels that I know have been central to the programming of DrupalCon are focusing around tools, technology, all the specifics of how we're approaching major rebuilds, projects of that nature. And, you know, a bit of what we're wanting to talk about today is actually beyond just the specifics of tools and solutions to all of the fun change management, process management that really is, I think, the hardest part of our jobs, oftentimes in navigating large scale projects and redesigns. And so I wanna talk a little bit about kind of what I see as the state of the, you know, dot org redesign is what we're saying. And again, we kind of have a little bit of a focus in leaning into nonprofit sector, of course, given the specific use case of MSF. So what I like to talk about is, all right, we're all in this, you know, ideal mindset before we embark upon a major redesign or project for our organizations. And we kind of begin with that ideal. So it's the ideal, it's a user first mindset. We're gonna approach it with the best in class design and tech solutions. We're gonna have empowered lean teams, agile data driven approach, run by those with real expertise, well-budgeted and of course, optimized over time. In the reality, I think for most of us who've been a part of website redesigns of which I have spent about the past 15 years playing many roles and from project management to the kind of senior relationship managing with our clients is obviously a very, very different story, which is lots of contradictory opinions, little process or empowerment for brokering consensus. Stakeholders rarely looped in as consistently as we'd like, probably under budgeted more than it should be relative to other sectors of the organization. And then the most critical point is, you know, we oftentimes look at these major overhauls of web and platform experiences for our clients on, let's say every three to five year cycle tied to some big RFP or it's kind of like your one shot to try and really approach how to improve the experience.  It's like you do it once and then you just, the organization overall is not thinking about the continual investment and maintenance of it. It's kind of a one time thing that you do every three to five years. And then it just really doesn't have the kind of central approach to iteration and optimization over time that ideally it really should. So what that leads to is what I call the bento box effect where you have a really complex organization and everyone on that website gets their own little square. It's sort of a consensus building exercise of how do you, how does everyone cram in that one thing they need every three to five years? And so I think we all know a lot of websites that look like that, a million little boxes and every team has their own little portion of it. And that's just a natural reflection of sort of the complexity of consensus management and stakeholder management in big projects like this. So, you know, in essence, what these cycles of redesigns look like is sort of like this. Every three year cycle or so, big website design project, website implemented, then a cycle of neglect. And then we gear up again and do the whole thing over again and then we slide back down into that kind of cycle of neglect. And it just, you know, we keep doing this and needless to say to all the people in the room that's preaching to the choir, we all know that this is a just, you know, crazy way to think about this central piece of the experience for our clients overall. So, Blue State's mindset is really, you know, how can we go from this, which is frankly the reality for most organizations, to this, which is not getting away from still doing major overhauls and redesigns every, you know, every so often. But how do you kind of build in more of a continuous cycle of iteration and optimization in the chapters of time in between? That is a major mindset shift. It's a major organizational shift, process shift. And then also a budgeting shift too. I think that's a big, big part of why we are where we are with these things only being approached every so often is oftentimes a financial reality of that too. So we'll touch on all of those things about how we work with clients like MSF to try and shift that mindset and frankly approach the website in the same way that we would email programs, social, paid media where endless amounts of resources and time often are allocated to those areas. And like we'd never dream of launching an email program and not interrogating and optimizing and testing that continuously. And the question really is why wouldn't we be building a culture of understanding of our websites oftentimes, you know, our websites often being as central to the outcomes for organizations as any of those other channels are. So with that, I'm gonna hand it over to Taylor again to talk specifically about how we did that in partnership with MSF USA. Thanks. So yeah, a lot of what I'll try and do is use our project as just a way of kind of building this example or drawing these connections. Like how do you kind of socialize a user first sort of mentality across stakeholders? What's the reason that you're doing that? There are so many things I could talk about. There's only so much time, but I really wanna leave space for a Q and A. This can be an open thing. I wanna hear about your experiences too. Any questions? You can share any challenges that you've had about how you manage stakeholders, how you need to try and build consensus in your organization. We can commiserate a little bit if we have to. But okay, I'll dive right in. First, what are we talking about? Who is MSF USA? Well, MSF, international movement, we often say movement, so I'll be using that for the organization shorthand, has 25 associations. MSF USA is one. And while I think they're, before my time, I've been in my role for almost two years, there was some consideration or inquiry into whether we'd want to unify all of the web properties for these associations, use a shared framework. As it stands, these are separate entities on the website in their own governance, on their own stacks, et cetera. So we are talking about doctorswithoutborders.org, which is the web presence for MSF USA specifically. You know, while all the funds we raise can go anywhere internationally, we are communicating primarily to a U.S. audience. We are fundraising primarily from a U.S. audience. We are recruiting primarily from a U.S. audience on doctorswithoutborders.org. So I don't have the whole tail of the tape, but I think the web presence for the organization is mostly mirroring how the fundraising is working as it currently stands. But who knows where we'll go in the future, especially in learning all that we did about the things upcoming in Drupal. So what's the website for doctorswithoutborders.org?  And the governance of it is similarly, you know, spread across many different teams. On the one hand, there are lots of communications needs and goals. You know, it's spreading awareness about what's happening in the movement, what's happening in operations, what we're doing, bearing witness, you know, saying what we see in the field impartially, holding entities accountable. This is a part of our charter, something we need to do. And so in that way, you know, the publishing that we're doing on the website is actually a critical function of what the organization exists to do. Similarly, you know, all going hand in hand, reporting on the operations to our U.S. audience. And also I wanted to include this, you know, holding the movement accountable as well. It's a space where we want to ongoingly publish, you know, things about self-inquiry, being critical of ourselves, making sure that that conversation is out there too is something that we want to have the space for on our website. So these are communications kind of pillars or goals. Development, not software development, but of course fundraising, I'm sure you're all familiar, is another critical need for the website. It's raising funds for the medical humanitarian aid that is being delivered around the world. It is providing resources to the donors, you know, that specifically the development audience, potential and existing donors may need documentation, instruction, support, and then also cultivation for some of those kind of one-to-one relationships we have with major givers, those sorts of things. The website is often used as a step in that process for kind of one-to-one communication. Field HR is another critical need, while over 80% of MSF staff are actually hired locally in the countries where they work. This is kind of a misconception that we want to do away with, you know, that everyone that works for MSF is a volunteer who's flown from a Western country elsewhere. That is not the case, although it is kind of a prevailing misconception, but I want to note that here. There is still though a need for us to recruit international staff to fill any gaps that we might have in the operations where we're working. So it is still a critical need for the site, of course, to be getting recruits who are paid staff, by the way. And there's a whole lot of other needs. Domestic HR, meaning recruiting and hiring for the New York office specifically. We have events teams, student chapters, and the people who manage those relationships. Advocacy, programs and operations, a medical team that actually publishes research. And as an internal resource, this is something I was actually a little surprised by when I started the role. You know, the website is constantly used as like the record of truth internally as well for people to understand the history of what we've done in areas, to understand our stances on sometimes complicated subjects. So this is all to say that there's a lot of things the website has to do, and governance then is spread apart in many different ways. Certain teams own certain pages. And the one thing I wanted to note too is that there is a very cherished culture of debate in the organization. We don't want to mince any words when we're debating things, when we're trying to figure out what the right approach is. But obviously when you're working on a website or an application, sometimes debate is a little scary. It can be a hard thing to manage. And I bet you all have some experience in that. So when we started, you know, we thought that we would focus on experiments, you know, in kind of smaller areas of the website to raise conversions, that being the goal from the start. But we really thought that after, you know, talking to all of our stakeholders and honestly just going with our gut and seeing what the website was, that none of these pillars were kind of being delivered on. We weren't meeting their goals. By trying to do so many things, nothing was quite sufficient across all those different pillars or teams. So instead, we pivoted to build a better UX and UI foundation to make a better communications experience, to make a better development experience, feel HR, ultimately to make a better visitor experience. And this is the thing we really wanted to socialize and have people understand at every level of the organization is that this was what we wanted to accomplish by embarking on this project. And that segues into how you can undertake change management. We wanted to align on objectives and KPIs ongoingly to be sure that everyone understood why we're doing what we're doing. We wanted to ensure that the highest level stakeholders are aligned on goals. And of course, you wanna go through that debate upfront because you'd much rather surface and resolve misalignments early than see the symptoms of that later on when it actually turns into scope creep, more expenses, hard pivots. So while it may sound like very general to say we want to make the website a better visitor experience, you need to have goals that match your stakeholder's place in your organization, match the level that they operate on. Because something as general as that can have real meaning to someone who's not so close to the project. And there are KPIs, accordingly will be some of the highest level ones, overall revenue, paid views, things like that. But this needs to ladder down through the organization. When you get to the specific teams that have governance over specific pages, they're going to have narrower, more specific goals in KPIs too. And you want those all socialized and you want them to kind of ladder up into each other or be like Russian dolls where if you have any sort of debate or disagreement at one of the lower levels, you know you can lean on the people one layer up to help resolve and arbitrate. But having that, the goals confirmed goes very far, obviously. Kind of what I was saying, once you're aligned on goals you need to understand not just who like the ultimate decision makers are if you do need to escalate up through the organization, but you want to identify more specific supporting roles. Who's informed, who's consulted. Many stakeholders can be involved as subject matter experts, participants in surveys, reviewers of design and everything if those lines of arbitration are clear. But hopefully through some of the things I'll share and as the next note, like you don't need too often to resort to that sort of escalation. Because this third point is maybe the most important one to me at least or where I saw kind of the most payoff in how we manage this project is that we wanted to really socialize this notion of being user centric or putting users and visitors first. So I said, socialize user first consensus building, like make it known that this is kind of your decider. The ultimate guide in swing boat, you know, is what your audience wants. And that you can really manage stakeholders and keep them along for the ride and make them have buy-in in your project. If you're engaging them by educating them about the decisions that you're making, educating them about the techniques you're using, the conventions in the industry or space and what you're doing, that's a way of keeping your stakeholders involved. And frankly, it's a way of priming them to the work that you're going to do and the solutions that you're going to deliver. I think that if we had reached and finished the project exactly as it is now having done it without involving stakeholders, if people saw it today, they wouldn't be happy with it because they weren't involved. They might see it and say, like, where did this come from? But they were involved. We socialized the practice and everything that we're doing. And I think that's why people are so happy with it now. So one note though, is that we wanted to build the project or structure everything around this notion, this goal of having the space and room to take stakeholders along for the ride. And so the way that we structured the contract was through an annual retainer for a website evolution with a bucket of hours and no fixed deliverables upfront. There are some other things too that we did, such as kind of decoupling design sprints from development sprints. We wanted there to be a healthy amount of space between when we design a component and when we actually developed it because by having discovery with so many different stakeholders through the whole project, we knew we'd want to revisit a component's design. We would surface and discover more use cases than one teams. And so by spacing things out, when we were developing them, we didn't have to make hard pivots. We were able just to expand or create more flexibility in the designs before we made too hard of a commitment. And I should say too, maybe this is better for the end, but a lot of this too, I think is something that you can do as an internal stakeholder. It didn't require me working directly with the blue state team to do a lot of this work internally and taking them along for the ride. So I see it as just wanting to have this space in your role in the empowerment, the time to do all this people work, frankly, that can help you have success in your project. All right, so I'll fly through these. Some quick examples, I think we're doing okay on time actually, but some examples of specific things we changed on the website and how this kind of ties back into the socialization, the stakeholder work that we were doing. So first, the navigation and information architecture, the deep bento boxing, as delicious as those look. So this is the old site. This is the old homepage and a snapshot of the navigation. It's a lot of menu items. And we kind of knew from the get go that this put a big burden on the visitors to the website that if they were looking for some specific content, they had to parse through a huge number of items to try and find it. It's a similar thing underneath all of these different main labels. Sometimes there are even, you know, sub-sub menus appearing afterwards. And it reflects that, you know, dispersed kind of governance of the website, you know. There are so many different teams that knew they had to have their content on the website. And instead of thinking, where does it fit? It's just make a page, add it to the menu. But it doesn't lead to a very navigable or intuitive experience for the users on the website. Some things too semantically, you know, are just kind of tricky. You see, there's links for support us, take action and donate. But what is the difference between supporting us and taking an action is donating not both? You get the picture. So what we landed on, if we look at a snapshot of kind of our new homepage and navigation, something has way fewer items. We wanted to introduce things like labels, you know, contextual clues to increase the information sent, you know, give people clues about the content they'll find in these subsections. To make it, you know, just a simpler thing to glean. You know, people don't have to try going into so many different pages to find what they're looking for. The thing I really want to call out though from kind of like the stakeholder management perspective is that we cut a lot of content or we consolidated it, we moved it into other pages. Like, there is no longer that designated space for press room, for a video page, for the research. They were reorganized, some of it was cut, but a lot of it was moved to different areas so that we have just clearer lanes for users to navigate through. Like clearer user journeys where we're actually building a path and sequence to the content that we're organizing. And we were only able to do that by getting that buy-in on the goals that we had for the site on that visitor-centric kind of vision. That was the thing that made people okay with hard choices of cutting or parsing down content or moving it or inter-tangling it with another team's content. It was all for the sake of making that clear user journey for visitors. A specific example too in how we wanted to socialize UX best practices to reach a better end. You know, in that example of the previous main navigation, there was a very prominent careers link in the main navigation. And the field HR team and domestic HR teams, when they saw that we had removed that from the main navigation, were understandably concerned that this would lead to fewer visits onto their pages, fewer views. But, you know, it is a convention we were able to show this to our stakeholders that across pretty much every industry now on the worldwide web, you'll find, you know, links to recruitment or jobs in the footer and sometimes in this top right kind of, or top left like eyebrow position. And it was after they understood the conventions and best practices that they were okay with us doing this. But we had plenty of time, you know, to take people along for the ride and really teach people the reasons behind the choices we were making. And just a quick note, you know, we actually did user testing to validate the new approach. We asked users, you know, where would you find this piece of content, compared it between the old navigation and the new and got really tangible data that showed the improvements that we could expect. And we did make alterations to our proposal, you know, based on that. Okay, another thing, critical homepage content. I'll fly through this. The old homepage had a lot of news and stories content which is critical, something that we want to include and have kept. But you can imagine, you know, stakeholders within the development department, we'll see that this is lacking something that has like a clear appeal or fundraising ask. And the changes that we made, I think, produced a lot of win-wins. And obviously that's a great thing to go after when you're managing a project like this is surfacing what can be shared wins across different teams. When we're thinking about what are the gaps here though, what was lacking on that homepage? Well, we actually had evidence that showed this is the internal site search feature that people could not find a mission statement. You know, for someone that's unfamiliar with what our organization does, this is of course critical and something we want to introduce. It's something that is a shared win across all departments if we can actually get people understanding of the work that we do. This is also reflected of course in the data we have in Google searches and everything. So if you scroll below the large image at the top of our new homepage, this is the new component that we introduced, something that actually has a clear statement about what we do, links people into upper funnel content, what we do. So already kind of building in more paths for users that are clear. And it introduces impact statistics and statistics around how we use funds that really is a shared win across both departments. You know, impact statistics being something that is the communications department really cares about but how we use funds, we know potential donors need to see that information when they're considering whether or not to support us. So leaner content and new calls to action. This is a big one. If we look at an example of a old country page, here's the country page for Syria. After the large image up top, you get into a lot of content. So if you scroll down a little further, you'd see something like this. And you could actually scroll through multiple viewports or full pages worth of scroll and just continue to see something like this. It's a lot of text because we have a lot we need to share and be very specific about what's happening in these different environments. If you reach the very bottom of the page after, again, multiple viewports worth of scroll there, here's something that would stand out to a development stakeholder as being lacking. This call to action is just links, hyperlinks added to the bottom of the page that obviously is not going to stand out very strongly to someone visiting the page and engaging with the content. And sure enough, this helped us get buy-in from our communication stakeholders to make these changes. If we looked at like scroll mapping, we could see that the vast majority of users on the site never actually reached those CTAs. And one thing I should tie back to when it comes to the shared goals and how you need that to help arbitrate the work once you get into the specifics. Up front, we had asked all of our stakeholders to confirm for us what are the main things this website has to do. And the communications department, field HR department, let alone development all agreed that raising funds is the most critical thing this website must exist to do. We need those funds obviously to do what we do out in the field and provide the life-saving care that must be delivered. So because we aligned on those goals up front, it made it much easier to harken back to that, get people to agree and confirm have buy-in and the changes that we'd make to this page. So a quick look at that. This is what you'd see kind of the top of the page. You notice wanting to make things kind of more graphical and stand out, introducing styles that are different from other content types on the website that you still have kind of the same pattern. But then again, it's kind of like a shared win is we found ways to address the needs of multiple personas coming to the website. So the development persona is often someone who's visiting the website who came from an email or who might have came from a social network. They may be in a mindset that is more operating on a quick kind of scan level. They want to see the summary information and get through the page. They may already feel compelled to donate after getting kind of a high level synopsis. But for that communications persona, we also need to address the needs of a visitor who wants the entire story, who does want to understand all the nuances of what we're doing. So a component like this is a win for both teams because it can shorten that scroll, make things more scannable, but we don't actually have to parse down the story and the needs of those stakeholders in the communications department. I'll say too that all these components have many use cases across the whole website. This is not something that we designed to operate and work only on our country pages, including that kind of image model below that has the statistics next to it. These all of use cases have crossed both departments in many areas of the website. So because we had stretched out discovery, we were able to deliver or design UX and visual design components that satisfied many, many use cases. It just made it an efficient use of our time and unlocked lots of content work later on. At the bottom of the page, we introduced a new call to action kind of system. And the thing I'd call out here is that this is one of the hard things for communications to accept sometimes. The thing that we're always hesitant to do is to place CTAs that could infer restricted giving, meaning we don't want someone on the Siri page who makes the donation to think that their funds are going directly to Syria. That would be, you know, we don't want to accidentally make the wrong impression when these are unrestricted funds that we can use anywhere in the movement. So it was through educating our stakeholders and kind of the techniques we can use in visual design where we got buy-in and people to accept this kind of new design where we use the visual elements to really separate it from the body of the text on our different article pages, on country pages. And that got people really accepting and on board with what I think is a much more kind of dynamic call to action that can really stand out to users and make a good impression. And one thing I'll note is that the vast majority of content was actually left alone. This was something that we decided to do pretty early up front as a way of streamlining a lot of the work that we were doing. You know, we really wanted to focus on the information architecture, giving ourselves a strong new foundation, organizing the content we had, knowing that so many people can get hung up on the messaging, on the words on a page. We really wanted to focus on kind of the system that we were building, and that has unlocked lots more optimization for us to do on the content side. So what's next? Like I said, you know, components were designed to be flexible, so now we can have a parallel work stream that works in content with the new components that we've built unlocking a ton of new things that we can do. And now that we have what I'd call, you know, a tightened information architecture, you know, it gives us kind of constraints to work in. People are thinking about how can they collaborate to improve on the areas or the subsections we have instead of thinking, I need content, so I'm gonna make a new page, and I'm gonna add it to the menu. And I'd be remiss if I didn't know that, you know, content work doesn't require development time usually, and that can be a great way of getting wins with stakeholders. Now that we have this kind of new baseline, we want to measure the effects of what we've changed. We want to understand what kind of the new performance levels are across the website, and react accordingly, you know, with new hypotheses, new tests to run, and ultimately changes to make. But that's all simpler now that we have better defined user journeys on the site. And again, the ongoing, you know, socialization of techniques, best practices, and this user-first ethos. You know, everything can be more efficient if you have that buy-in and knowledge across many teams. So that you're cultivating, you know, holistic approaches and collaboration to avoid siloing and bento-boxing. Instead of someone thinking, my content needs to go on the site, so I'll add a page. They can see what these new lanes are, what the new information architecture is, and really keep top of mind, like these personas we have on the site, and figure out where is their content most relevant? Where does it make the most sense, and who should they collaborate with? What are their owners to make it happen? And with that, I'll hand it back to Katie. So we wanna just do a wrap up of a few of the things that we feel are like principles, key takeaways, things to always be coming back to and reminding ourselves when we approach this category of work. Again, not even just about the specific solutions that MSF was able to arrive at and through this process, but things that I think are just universals for how to approach in the mindset of these kinds of projects. So one is really think about designing your project with Consensus Building from the very beginning, and really thinking about what's the core group that you wanna have pulled in from the, like there's almost no way in which you can do that too early in the process. Websites, website redesigns are product, I mean, these somehow become the most political fraught projects of all the projects that I work on with clients, which span well beyond website work. And it really is because it's this one time where people have a shot to have their portion of their initiative featured, and we know how those politics can play out very, very quickly on the limited kind of one shot of presenting your organization to the world through the website. So that's one thing I think is just, even if you make a different decision, if you've really thought about how to bring in the right stakeholder from the very beginning, you're gonna save yourself so much pain in the long run of having to kind of retroactively find a way to address those concerns of people feeling as though their organization wasn't heard or left out in the process. Second, really don't skimp on educating people about why a certain decision is the right one. And I think showing, like show, don't tell is a very, very important thing here. What Taylor talked about, like just even being able to kind of show, we'll look at these other organizations or these other brands, and sort of the way in which these conventions are evolving to kind of assuage those concerns or feelings that people would have, is always gonna go so much better than just saying, this is why we need to do this. And I think that's just intuitive, but yet we, in the rush and limited time and capacity that we have around these projects, just oftentimes don't create a lot of space for that. And then just further those rifts and divisions that sometimes can form internally around projects like this. Building the case for ongoing investment with performance data, so one thing we didn't really talk about but I think is generally true is, we're really close to the numbers, for example, on a fundraising side for many of our clients about how many dollars are raised from email versus paid versus website. And while it's not always universally true, usually the website is bringing in substantially more than any one of those other channels, but yet again, the resource investment for that doesn't always reflect what it should be, where there should be the same kind of resources and investment approached with the website. So know your data, know your performance, own it, socialize it. At the end of the day, senior stakeholders listen to this more than anything. And I think that that's something that we oftentimes forget to champion, particularly around the website channel, regardless of what your organization's goals are. Really be unafraid to show that data and then hold yourself accountable to that data ongoing as a way to build support for further investment. And then I think this is a really important thing if you are able to shift the organization from the mindset of that you have one shot, one redesign to get it right. That's a really great way to start to remind people that it's not as though you have just one shot to get it right either. And so that can really diffuse the attention or the conflict that can arise around these projects. And I'm kind of making it seem as though these are terrible projects. That's not it. It's just we know that these things can arise and we've probably all seen it. And so I think that just reminding people that the launch of the site is just the start and that that is not a set and stone thing. So I come back to that point time and time again when we're debating, trying to arrive at the perfect decision. It's like this is not about that and we have to shift our mindset. If you think of a big brand like Nike up the road, they would never think this is our one shot to get this one feature right on the homepage once every three years. That's just not the way the rest of the world thinks and we have to do a better job of socializing that in our own organizations. So with that, we've wrapped up our portion. We've got about, I think about 10 minutes for any questions that folks have. So happy to field anything from the crowd if there are any questions. Yes. Yeah, thank you. So the question to repeat it, yeah, was around user testing and whether or not we were running user tests kind of before, during and after kind of when we were doing these tests to kind of give us data to act on. Is that right? Yeah, there was a wealth of data we had for the project but often kind of unfiltered that we wanted to surface insights from, glean from, you know, things like what's available in Google Analytics, doing kind of a page performance analysis to see how users were navigating through the website and that really surfaced like upfront, this clear picture that people were entering the website from a million different places and they were quitting from every one of them. There weren't kind of clear funnels for people to move through engaging with content. So a lot of the upfront work to kind of create a problem statement was done with data more so than direct user testing. But once we got into designing components, it was especially that navigation that we showed that also being the IA, like the real kind of organizing structure for the site where we wanted to validate a new approach first. Those are the two main areas where we started with along with just making sure that we're doing all sorts of, you know, accessibility testing for the new designs that we had. That we all wanted to be very confident in while getting to the launch of like these changes. Now that they are live, what we want to do is assess more clearly, like how people are moving through the site, wanting to get into more anecdotal research, both with our internal stakeholders and visitors to surface the new hypotheses. So given that we haven't changed too much content just yet, we felt confident that we were just doing or covering the bases for kind of a new organization on the site. Now that we're gonna get more into messaging and further optimization, we really wanna get into some anecdotal research, yeah. Yeah, the question is how are we doing research? Is it real time on the site through a modal or a pop-up? Is it anecdotal? Different areas of the site, we've run different kinds of tests. So for example, the ways to give section of the website is obviously something kind of in the development department's governance. We've run lots of surveys there through existing third party tools to create pop-ups and ask people whether they're finding what they need, what their experience is, and inviting them for focus group sessions. We're often using other channels too, like our email channel to invite super supporters to be involved in focus grouping so we can continue doing work there. So it's a mix of both. There's lots of insight we can get obviously from analytics and parsing through everything there. In areas where the persona is so specific or clear, that's where we're really excited to get people into focus groups. The people who are navigating those ways to give pages, for instance, are a very specific kind of subset of donors. It's distinct from the first level donors we have. So yeah, we're trying to kind of scale up or scale down, get more or less bespoke in how we're doing research, depending on the persona we're targeting. Yeah, thank you. I'll actually add one. Can you guys hear this okay? All right, one other thing I'll say, not with MSF, but with a couple other organizations that I've worked with over the years. The other thing that we've done is try to set, what I would describe is, I mean we actually use this phrase and I think it's helpful. It's called a learning agenda, right? So what are the things that we might have hypotheses about post-launch, that we wanna run longer term, tests and experiments on, leveraging tools like Optimize Leader Run, specific tests, and even using tools like that to make minor front end changes that don't require a lot of reworking of the underlying architecture of the site. So a great example of this is many years ago we worked with the Nature Conservancy. There were a handful of things that we were curious about changing on their homepage, but didn't wanna make anything that was potentially gonna negatively impact fundraising performance, so not going in and making larger changes. They didn't have the resources to do a big redesign. So we ran a number of concentrated tests around some high traffic areas of the site that we knew could really drive performance, ran those tests re-optimizedly. It wasn't even necessarily a formal user research experiment, but was able to really give us the data that we needed to know if we were safe to go ahead and implement some of those changes in between larger redesign cycles. And that, I don't know the top of my head, but resulted in some pretty substantial increase in your revenue for their end of your fundraising, for example. So that's another great tool that you can use when you're not necessarily positioned to have access to regular ongoing user testing. One thing I'll add is that it was a real benefit of having ongoing discovery through the whole project as well. That helped us to surface insights from lots of different team members at different times. In my experience past, when I was agency side, many products would have very concentrated upfront discovery with a limited set of stakeholders. But in working on this project, we may have been months in and we talked to a specific team member who's aware of a specific set of market research that we surface and ends up generating or highlighting some very powerful use cases that we wanted to target against or helps motivate our content strategy in a certain area because we realized that we did have this documentation on hand that said, they engage with this kind of content best and that sort of thing. I think having this space for that discovery over time and all that stakeholder involvement really made sure that we weren't missing things for us to kind of build into the UX that we're delivering. Maybe we have time for like one or two more. We've got five or so minutes left. If there's any other questions. So what kind of like all of the things I said on the most, what do you think about that? Yeah. Oh, sorry. But I could also experience with the NGLs and you know that some of the programs I would ask are in different ways and people when they need to be in the same structure it's very difficult for them, I think. Yeah. So the question is kind of around, you know when you're having an organization that has its own website or property in general, brand expression, but there are many different sister organizations doing the same thing. What arises from differences? Is there a tension or is there a need to kind of spread and share what's changed? How is it navigated? That's kind of the general question. It's interesting. I'll say first that we absolutely want to socialize and share like a lot of the work that we've done because we could see it being creating strong improvements in different other areas on some of the sister sites. And I think that the ways that we could socialize that and get that adopted is through a lot of the ways that we've got buy-in from our internal stakeholders. If we are really able to say through evidence and data that we are seeing better performance or a better user experience through the design changes we've made, then absolutely, I think there's a much greater chance that it will be kind of accepted and adopted and that will make a more consistent, you know, brand across the board. And that is all sorts of benefits in terms of just visibility, association with our brand. For instance, you know, one of the things that we changed is that all of the headers we used to have on our site used to be white text on a very red rectangle. And what do you know that looked exactly like our buttons? And so it's very easy to like make the case for other organizations or other websites, you know, to maybe create some distinction there, avoid rage clicking and a confusing user experience. So some things will be easier to socialize than others, but I definitely see there being benefits and want to help make consistency across the board. Did it, was there any like more specifics you had in mind or wanted to explore? Sure, thanks so much everybody. Thank you all.


students, I would now like to explain to you how to utilize the probability generating function in order to obtain the probabilities of a discrete distribution and also later on how to find the mean and variance of the distribution through the probability generating function. The relationship between the individual probabilities and the probability generating function is as given in equation one that you now see on the screen. It is expressed as follows. The probability of x is equal to k is the kth derivative of the probability generating function and after taking the derivative, we have to substitute in that z is equal to 0 and then this thing divided by k factorial. So let me give you an example to explain this point. Considering the probability generating function of a Bernoulli random variable, when for example, we are tossing a fair coin only once, you know that the probability generating function for this case is given by 1 by 2 plus z by 2. I want to find what is the probability of x is equal to 0. So according to the formula that I have just given you, I have to find the 0th derivative of the pgf the probability generating function and then I have to put z equal to 0 in that and then I have to divide that by 0 factorial. So students, what you have to do is to just simply put the value of the pgf, the expression of the pgf over there. So that is half plus z by 2 or 0 factorial saves you have divided and now you keep the value of z or z as 0. So what do you get? You get half plus 0 by 2 divided by 0 factorial and that is equal to half. So you know that the Bernoulli random variable that we are considering right now, the first probability is equal to half. So the formula is the same as the answer that is exactly the same. Similarly, the second value of x is equal to 1. If we want to get this probability through pgf, then according to our formula, we have to take the first derivative of the pgf and divide it by 1 factorial and then we have to put z equal to 0 in that expression. So in this case, what is the first derivative? Half plus z by 2, the first derivative, 0 plus 1 by 2, 1 by 2 divided by 1 factorial, that is 1 by 2. So once again, you have seen that the probability x equal to 1, the answer that you should have got is half. So this is a simple example to illustrate how you can generate probabilities from the probability generating function. After this, as I said earlier, I would also like to tell you how to find the mean and the variance through the probability generating function. Expected value of x, the mean of the random variable x, is given by g prime of 1 minus, as you can see on the screen. Before I do anything else, I have to explain to you what is meant by g prime 1 minus. And z instead of 1 minus, we are taking the limiting value of the prime z as z tends to 1 from the left hand side. So probability generating function, that is given by e raised to lambda z minus 1. Obviously, it will be by simple rules of calculus lambda e raised to lambda z minus 1. So the limiting value that z is tending to 1, that will be lambda e raised to lambda into 1 minus 1, that is lambda e raised to lambda into 0, that is lambda into 1 and that is lambda. You already know that the mean of the Poisson distribution is equal to lambda. So this is again a simple illustration of how the mean can be found through the pgf. As far as the variance is concerned, my dear students, the formula goes like this. The variance of x is equal to g double prime 1 minus plus g prime 1 minus minus g prime 1 minus whole square. G double prime means that we will take the second derivative. Now instead of z, we say that z is tending to 1 from the left hand side. So g double prime 1 minus comes out to be lambda square because the other part, that becomes equal to 1. Lambda square, your value is equal to g double prime 1 minus. Plus g prime 1 minus, lambda minus g prime 1 minus whole square, and we are left with the variance of x is equal to lambda. The mean and variance are equal.


Hey, this is Brett, and this 2018 Ram 3500 True Cab Long Box Dual Rear Wheel Laramie is stock number 14293Z. I am here at Summit Automotive in Fond du Lac, Wisconsin, you're new and used heavy duty truck and specifically Ram headquarters. This 2018 Ram 3500 has the 6.7 liter high output Cummins diesel. In 2018, those produced 385 horsepower and 850 foot pounds of torque. It's paired up with the 6 speed heavy duty ice and transmission. This truck has been fully safe and inspected by our service shop as a fresh oil and filter change. All the fluids have been checked and topped off and this truck is 100 percent ready to go. I'm going to go all the way around in this video inside underneath, start it up, take a look under the hood, show you all the options and just give you the most accurate representation that I can of the vehicle. Bright white clear coats of color. I shoot all my videos in 4K. If you like the video, subscribe to the YouTube channel, click the bell notifications to get updates on the videos I do each and every day. As well as having access to one of the largest catalogs of vehicle in heavy duty truck walk arounds on YouTube and stay current on our vast and ever-changing inventory here at Summit Automotive. This one comes with the really nice 17 inch polished aluminum wheels. They are in excellent condition. You can see these scuffs and scrapes on there and it has some really nice Goodyear Wrangler Workhorse AT tires, these are LT 235 ADR 17s. They have a substantial amount of tread left on them, I'd say probably 80-90 percent of the tread left on those tires. Framing on your body is exceptionally clean on this truck. This is a clean title history, clean car fax and it's always been old in Indiana. Front fender is in excellent condition, no dents or dings on there, you get a projector lamp, LED running lights, factory fog lights and the front bumper parking sensors, take note on that front bumper, no dents, no dings, no scuffs, no scrapes. Lower valence is in fantastic condition as well. You get the chrome trimmed grille and that hood is absolutely perfect, no major dents or dings on there. And you do get cab lights up top. That extra black piece up there is a GoPro holder, so that's kind of neat. Passenger side front fender, no dents or dings on there. And the passenger side front wheel, no major scuffs or scrapes, looks really good.  This is a 2018, but take note of how clean the body is, how reflective and mirror-like that paint is. I take these HD videos so if you're far away or even if you're close by and you just cannot make the trip down but you're still interested in purchasing the vehicle, you can see the truck, hear the truck and have confidence in the vehicle that you're looking at before you even get here, so when you do get here there's absolutely no surprises and you can make a smart and informed buying decision wherever you're at. Now if this video helps you make that buying decision, let your salesman know that you saw the video, that it was helpful and that Brett sent you. As the nice factory chrome step-ars, take a look at this, duly tell me how clean that is. It still has a 3M rock guard on there, didn't see any major dents, didn't see any major dings, looks really, really nice. Back wheels are in very nice condition as well. And the back tires have just as much tread as those front tires, frame and under body looks really good. You get the nice big plastic wheel well liners back here and the frame and under body under here looks really, really good. Has all the remaining factory exhausts, so it hasn't been altered in any way. And all the rockers, cad corners all look really great and no corrosion on them. Really a nice truck for a 2018, fender flares on the back here as well. Coming around to the back of the vehicle, the rear bumper is in fantastic condition, no dents or dings on there, looks really good. It has the backup parking sensors, full towing package of course with the receiver hitch four pin and seven pin wiring. Tailgate's in really nice condition as well, I didn't see any major dents or dings on there. And it does come with a back flip fold up tonneau cover, and that's in pretty nice condition. It's got a little bit of wear up front from getting folded onto, but no major dents on it, looks pretty nice. Comes with a very nice spring and butt liner, fifth wheel gooseneck package, you also get the seven pin wiring back here and 2018 was the first year that you could get the LED headlights with the button back here. Very nice and clean back here. And that spring and butt liner goes onto the tailgate, which is very nice as well. Tailgate shows us nice and solidly, and as we go down the driver's side just as clean as that passenger's side, no major dents or dings on the box. Very nice condition, and for full disclosure, this back wheel just as nice as the rest. Cab and doors all look really good, so it does have the heated fold up tomeaus, built in directional signals, they fold up like so and in like that. Now you wouldn't believe me if I told you this, but the inside is probably nicer than the outside. Take a look at these seats, no rips, no tears back here, latch child safety system, these back seats look like they've never been sat in. You get the power sliding with your window, very nice condition.  Or if you've got pets, put both sides down, they've got a nice flat place to lay, and they're not going to get your seats dirty, you've got a storage area under there. Comes with some nice mother tech floor mats and in-floor storage with removable bins for easy cleaning, put ice and drinks in there. There's a receiver hitch reducer in this one. A cup of ice and drinks there, it's like you have too many coolers wherever you go, or if you're not in Wisconsin, just extra storage space. There are your heated seat buttons for the back and a 12-volt power point. Side current airbags on the front seats. Child safety locks on the back doors and the inside and bottoms of the doors, absolutely no corrosion on them. They look really, really nice. Here is the VIN sticker. No previously owned in Canada trucks here. Here's the tire and loading information sticker. Inside, the Laramie package gives you the tan leather bucket seats in the front. Seats are in really nice shape, no rips, no tears. On them, they look really good. Laramie embossed into the backrest. Memory driver seat with lumbar, leather tech floor mats up here, auto headlamps, power windows, locks, and mirrors. And these mirrors do power-fold in. I always like showing both sides, so you know that both sides are working properly. We'll hop inside, check out the models, the radio and everything that this truck has to offer on the rear. You can see that this one has the Laramie animation and the 7-inch LCD display. The instrument cluster is very nice and clean. This one has 55,393 miles. Digital spinometer, compass, outside temp, time, range to empty. You can change all those corners to read pretty much whatever you want. Comes with the heated leather wrap steering wheel, cruise controls on the right, Bluetooth and information center controls on the left. It does have audio controls on the back of the steering wheel as well. There's your shifter for that six-speed automatic action heavy-duty transmission. This one has the 8.43C radio. There is the factory navigation system and there is Highway 41, so you can see that is working nicely. Once again, always something you want to check on these trucks. This one has AM FM and Serious XM radio capabilities.  There's the back-up cam that is working nicely. Then you get all your different apps on here. This one does have a projection manager. I take that back. This is the 4C radio. The projection manager didn't come until the 4C radio in 2018. You can project your cell phone to the screen. We did a demo on an 8.44C radio. If you want to check that out, that's in the upper hand part of the screen with Android Auto. There are all your other climate controls. Turned out four-wheel-drive, push-button start. More tactile, volume-tuned and climate controls down here, factory brake controller, heated and cooled C buttons and steering wheel controls. Stability control, tow-haul, factory exhaust brake front and rear parking sensors, and a 115-watt plug-in. Heel-less entry with a remote start and passenger-side climate and seat are available. There are the speakers in the ceiling and this one has the power sunroof. There are your map lights, power side rear window controls and holding buttons for your garage door security systems and lighting systems as well as assist and SOS buttons in the mirror. We'll start it up and take a look under the hood. Starts right up. No check engine lights or anything like that. I would personally like to thank you for checking out the video today and hopefully from this HD video. We've had the quality condition options and of course, cleanliness of this truck all the way around inside out. All those lights are working very nicely. Under the hood we have a 6.7-litre high-output Cummins diesel, 385 horsepower, 800 and 54 pounds of torque. Engine base is very clean though, it's very smooth. Once again, this truck has been fully safely and inspected by our service shop as a fresh, clean and filter change. All the fluids have been checked and topped off. There is the emissions sticker and this truck is 100% I would highly recommend this truck for the quality condition standpoint. I'd ship this one back to Indiana, California, Texas, New York, Florida, wherever whoever is going to get this truck is going to be very happy with the quality and condition. To see more pictures of this truck or one of other 550 Union's constructs, SUVs, minivans, rainbows, half-tones, and filter turns, one-times, you and I that we got it, go to the website over there www.SummitAuto.com Full pictures and subscriptions are everything in the vehicle all at www.SummitAuto.com Thanks again for checking out the video. Remember to like, subscribe, and share on the YouTube channel. I'd really appreciate it. Thank you so much for watching. I'll see you in the next video. Bye.


Hello and welcome back to the craft box. My name is Brinton today. We're back on Wizard101 Um, I was watching Ki live as I Try to do every month. Um, and they released a new quest during the thing if you don't know. Um So, yeah, let's let's poppin and do it Oh, hello. You're that wizard everyone's always raving about, aren't you? I'm Renee. Nice to finally meet you I'm glad you wandered by headmaster Ambrose tasks me to survey the commons to ensure everything is on the level And I could use a hand if you've got a minute Could you take this range pole to a few different spots in the commons so I can record some measurements from this centralized location Just place the range pole down for a second or two at the spots I've marked on your map and I'll do the rest. Thanks. I appreciate it Okay, so we have to go and Use these range poles. I originally had a different video planned for today. Obviously, this is coming out tomorrow as I'm recording this but um, Yeah, so there's four range poles around the commons. Um And what seems to be an almost too perfect square I have obviously probably by the title, you know what I'm going to be talking about but um I am 99 percent sure this is something to do with a possible commons revamp or redo or redesign or Something to do with redesigning the commons of some form um And I think that's fantastic Honestly, I can't Wait for that to happen if that does happen that would be so cool. Um, and you get more of a sort of Feeling from the last bit of dialogue here Um, so that's where the four range poles are Pretty perfect circle fairgrounds behind these houses over here and over here Just cut not a circle square. Geez. I can't even geometry but like Yeah, perfectly encompasses the whole commons in there range poles are usually used by um Landscapers and builders I believe to kind of get like to know exactly where the area that you're Doing your work in is so I'm Honestly just assuming that this would be the same and I wouldn't be surprised if it was Thanks, that's all the data I need I should be doing more work here in the commons soon drop back by if you feel like helping out Oh by the way, maybe don't go around talking about how you help me survey the commons Don't want to start any silly rumors, you know, great Well, then I better get to work drawing up plans. Hopefully we'll talk again really soon. Bye bye And thanks again for your help. Okay, so let's just unpack the style of it. Um, First going to enough sound. Um, so we have Workup. Um, she's gonna work on drawing up plans. So obviously there is definitely some sort of Thing happening Because why would you make plans if nothing was happening? Um, something where was it? Um, don't want to start any silly rumors. Basically just Usually people would say this if you're kind of hiding something that is obvious and this is very very very obvious sorry, but like Yeah, and then uh, she'll be back soon. So obviously She'll be coming back with more quests. You also let's turn on the sound again It's a bit weird without it on. I'm you also get a range poll which looks really cool It is probably one of my favorite ones like It's so cool. Uh, let's just hop off the mount so we can see Um, like look at this. This is honestly that looks so cool I am definitely going to be stitching this on my life wizard because this is such a good This is such a cool stitch. I might even maybe on my death. I don't know It's more of a like with the green. I think it would be more of a life wizard sort of thing, but Yeah, it looks so cool. Um, but yeah, anyway, so I'm kind of hoping that they do I really do hope that they don't just update the graphics because I think they could possibly like redesign everything that would be really cool kind of just Flesh it out a bit, you know Redesign it have different areas. Maybe I don't know. They'll be cool Um, so yeah, that's kind of just this video really short. Um, but just letting you know what's happened Obviously I do all the side quests So I was going to do it and I've already done it on all my other characters just because the wand is so flipping cool And I'm going to be definitely stitching it on my life wizard. Um, I'm just going to add in here. Um, I Already finished the video, but you know, um, also in KL life. There was a, um, code, um Q a code. I can't remember what it was called. Um, I'll put it up on screen if I remember I should It will be in the description. Um, and you can redeem as many as you want. Um, and it gives an as designed um housing item, which is the wee little bug symbol In a painting I don't know. Maybe it is A bug reporting thing. I don't know. Um, but yeah, that was just something We're going to go have a look at that as well because why not? Why not? Um Let's put it up in this tranquil cottage that I have Um, not gardening this one. Where is it? Here it is as designed.  Does it? Yeah, wow. So yeah, it's also kind of crooked, which is a bit unfortunate But um, yeah, that's that's also what you can get. I'm still using the wand. It looks so cool. Um, but yeah So thank you for watching room to live a like and subscribe If you have any comments or things you want to leave in the comments about this do so I'm I love to hear your opinion on this. Um, but yeah Thank you for watching room to live a like and subscribe and if you've already subscribed press the little bell Sooner or exactly when I post another video and remember craft outside the box