Hey y'all, this is Jamie without a bounce with Jamie and Abby presented by Ashley. And today our episode is being recorded at the Graduate Nashville. It's an amazing hotel here off West End. You can check out the rooftop. Also, their coffee shop in the lobby is amazing. It's so cute. It is so cute. When we were just out there, we noticed the coffee shop had pencils. It was made out of pencils. It's just, the decor here is just absolutely amazing. It's so fun. But on today's episode, we had Talyn Lawan. She is the wife of Taylor Lawan, who is going into his ninth season as a tackle for the Tennessee Titans. And she was incredible. Yeah, one of my most favorite things to do is to learn about the wives and let people know they're not just their players' wives. You know what I mean? There's so much more than just being a player's wife. And like for Talyn, for instance, her and Hailey Hubbard started feeding Nashville. And she's a huge animal advocate. And it's just, it was amazing to get to know her as a person. Yeah, I totally agree. So we hope you guys enjoy. I'm so excited for you to meet Abby. And I mean, I've known you for seven years now. I was just thinking about the first time I met you, that Fred's. Yes. Yeah, I was pregnant, I think, with my first. Uh-huh. Yeah. I remember that. Yeah, it's a while ago. I love it. Now the girls. Now I got two of them. It's crazy. I can't wait. I can't wait to talk about the girls. Your amazing house, by the way. We drove by the other day. And there were cars everywhere. John was like, he better be at practice. That was for the girl's birthday party. Oh, that's funny. And Taylor's in bed before my kids are. So don't draw on the other three. Sometimes I'm like, I'm gonna call somebody and see if people are going to bed before their kids go down. Cause I think you're just trying to get out of this. Yeah. Trust me, we do now. I mean, John, it's night, 8.39 o'clock. He's like, can we go lay down? Like the kids are still awake. We can't. I mean, yeah. He's not the only one. I'm not gonna tell him that. I'm just saying, I'm like, he's dead. Seriously. Well, since I don't know you or your background or anything, can we kind of just start at the beginning? Like where are you from? How you ended up in Nashville and all that. Yeah. So I'm from Canada. I'm from a small town called Lake Country or Kelowna in British Columbia. And I was living in Florida for a little bit. And then I got scouted for modeling. I was around 17 or 18 at the time. Okay, maybe this is something I'm supposed to be doing and I wasn't really doing anything else with my life. So I was like, I'll just see where this goes. And it brought me to Nashville because I kind of had LA or New York and I didn't want to be a really small fish in a big sea. And Nashville was still the same networking, but I felt like it was more like a small town feel, which was more close to home for me. So I came out here and then I lived out here for about a year and then I met my husband. I was about to go sign my contract and then he followed me to LA. What? Yeah, proposed to me in five weeks. I thought we had to hear about that. Wait a second, there's so many details we needed from this story. That was in Florida when I got scouted and I got down my modeling kind of trail. I ended up in Nashville, I think I was 20. Okay. So I think I was in Nashville at 20. And you met Taylor then when you met 20? I met him once in passing because I met his mom first and I met him and he was like, she was like, don't talk to my son. He'll fall in love with you. I was like, okay, no problem. Right before I was about to move to LA I got in one conversation with him and then he followed me out there. Oh wow. That's crazy. It proposed five weeks later. Taylor wants something he's scouted. Oh my gosh. And then how long after did y'all get married? Three months. Yeah, so I got engaged. Three months from when we met. Yeah, we got married in April. Met in February, got married in April. I just met him and I was like, I'm going to LA. He was like, I'm coming. Oh my gosh. No, no, I didn't like it. Like I never liked, I didn't like the industry. I didn't like how you were talked to. I didn't like the girls, like just their mindsets was all very, just not me. So I had a hard time in it. I felt very kind of alone in that. And I was like, this is not what I want in my life. Like I don't want this. Like it's got to lead into something else. Like there's a different calling I have to have. And so there's this guy named Josh Gates and he goes around the world just like looking at different mysteries and stuff in the world. That's what I wanted to do. I swear. So I wanted to go on all these expeditions. So I ended up going to South America and did a documentary on animal trafficking. And yeah, I did that. And so I met Taylor in February, we got married in April and I did it in August. So you were the host of that, of like a series? Yeah, I'll tell you what, be 29 years old and watch yourself at 21 talk for a whole couple hours a little. I'm like, I can never tell anybody about this. I'm like, no one can do that. But no, I look at it too, but it's just like I'm so proud of myself for doing that. And the documentary, we put it down in South America first and it ended up like getting a law change to protect Andy and bears down there. Yeah, so I came back and I was gonna do another one about wolves and Yellowstone and then when came along and surprised us and now things took a little bit of a different direction. And I remember being like, I'll just take her, she'll be what six weeks old, I'll just strap her to me and we'll go to Yellowstone and it'll be fine. And then at six weeks old, I'm like, I'm not leaving my house. You're like safe space. Not happening. So now that's kind of on the back burner and I'm just enjoying being a mom. Oh my gosh, that's so cool.  How did you start with that love of animals? So I think I've just always loved animals as a child and I think most children do. I just never grew out of it. So then I think that I've always had a heart for things that don't have a voice or people or animals that can't help themselves.  I'm like, no, no, animals is my calling. And then you have kids and I'm like, oh, God, like now I just want to help every child in the world and it's so true. But I think it just comes from me. I just have a heart to want, I just want to help things that can't help themselves. And I just feel like we have such a responsibility to like take care of everything instead of just like every one. And that kind of goes out to animals. And I think with being in South America, you start to realize how much, even just like the little beetles there, like effect the ecosystem that like affects us up here. And so like when I just started seeing all that, I'm like, wow, there's just so much that we can do to help. So then I just That's amazing, that's amazing. So how many animals do you have? Oh, we've got 13 chickens, three ducks, one bunny, three horses and three dogs. You just got surprised with the horse. I did, yeah. My third horse. Oh, she's gorgeous. Oh my gosh. She is gorgeous. I cannot wait. She's staying in Arizona because that's where my husband is from. So you just go out there and ride and I've got two here and then I've got one in Arizona. That's so cool. So what kind of riding do you do here? So it's English, Charles. I'm learning English. It's just a harder way of riding and I think it's just a good foundation to start on because the only horseback riding I actually have in my past is bear back on some horse clanging on for dear life and hoping for the best of it. It's kind of like a ranch horse, you know what I mean? Like I've never done the proper like training. Yeah, so I'm starting now. I'm actually doing it with my daughter. So like on Wednesday, we will both go and we'll both learn together. Like I want to start learning Italian so I'm gonna do that with her too. So I'm trying to like start this thing where like we learn things together and I feel like it'll help her stay with it and it'll keep me accountable too. So yeah. That's so cool. Okay, so how old are your daughters? I got a five year old and a two year old. Okay. Yeah. I got one that looks exactly like me and one that looks exactly like Taylor. Do they act like? Uh, they're both like some. When is more me? She's very like empathetic and like softer and Willow is just. Willow is just a whole, like when makes me look like the best parent in the world? Yeah. Willow humbles me. I was gonna ask if you had that motherly like experience where you're like, I'm the best mom on your first and then on your second, you're like, Oh, never mind. I don't think there's does it. Like, yeah. Exactly. Yeah. My first was that and then my second was the easy one and I was like, okay, I kind of understand now like why people want a ton of kids. Yeah, it's exactly what I was saying. Like, I mean, I think I would go for one more but like if they were all Willows, I couldn't. Yeah, that's hilarious. I couldn't.  No fearless. Yeah. So fearless. And I'm like, she's, I wish Taylor could hang out with her every day because I'm like, this is your kid. You dig her. How's it been having him home all summer? It's been good. So I was in Canada for most of the summer for the first time in three years because of COVID. And so he came up with me for the first time.  So it was really nice having him there. But then he left and came back down for, he was probably down here for about three weeks before I was.  It's been, it's good to miss him. Yeah. He's like, it's having me. How did you adjust being an NFL life? It's a fun story, like how we met. But I went from like, my maiden name is Taylor and Gallagher. And I always try to like describe it as like, I thought Taylor and Gallagher and Taylor and the Juan had to be two different people. And so I had a bit of an identity crisis because I went from like, I was just working down here and I was going to go back home and like the whole family, like I have a big family and they're all there and my plan was to always go back. I never imagined living or raising children away from them. And then so I become this wife, like when a world went, I'm like, okay, I'm a wife now. I'm like, oh, now my wife has sent me in the spotlight. Like, what does that look like? And also now I'm pregnant and I'm like, oh my God, I'm almost like, what am I? You know what I mean? And I just had this huge, almost like crisis and then, but then it's hard to have a crisis when you're like, wow, I should be so thankful. Because like, look at all that I've been given in life. Like I have this husband who loves me and this beautiful daughter and we have all this freedom his job has just given us so much, but yet I'm freaking out. You know what I mean? Like I don't know who I am.   So, and then being, I was 22. You're young, yeah. How do you process all of that? It was just, it was like, it was really tough for me and Taylor's a really big personality. And what comes with that is it's really high highs and really low lows because he is so in the center of attention and he puts himself there that when if things go wrong, he's going to be the first person that's going to be torn apart for it. You know what I mean? And it's like, as much as he's this big, like tough guy, like he loves to be loved. And I think that's why he has this personality that loves this attention.  You know what I mean? But it's like trying to go through that whole process when we were both so young. It's like that was like, I think one of the biggest things in the NFL world where I was like, holy, like, what's happening? You're taking care of him and your baby and trying to figure out who you are. Yeah. And really still getting to know Taylor. Oh my God. That's what it was. Yeah. Don't. I don't, I don't want to go back there. I'm like, I don't want to go back to that time in my life. That was crazy. Oh my God. So I mean, I knew that was like, going to be like one of the things we talk about is like being the NFL website and reflecting on it. And I'm like, what does it mean to be an NFL wife? It's a hard place to complain because how could you? I mean, in all those aspects that you're given and the things you should be thankful for, but it's hard, you know, there's a lot of sacrifice that comes with it and your time is not now. Like your times is when they retire. Like you, you live in a shadow for as long as they're in this and knowing Taylor, he'll probably go into movies or something. So I'll be like, I'll be in the shadow for the rest of my life. But like, it really is. It's not like when I see like Ryan Casey, I don't know if you've followed with her. That's Jarell Casey. So he used to play on the team and he retired. And I just messaged her cause she's like come out with her own wine and she's just like won her first court case.  You know what I mean? And I'm like, well, that's a great example of like an NFL wife's life. Like you grind through it and you get through it cause it's worth it. It's so worth it.  It's your season. You know what I mean?  Do you feel like the pressure as far as trying to live up to what people think you should be like? 100%. Cause that I'm not going to lie. That happens to me. Well, I'm really careful as to what part of me I think I put out there because it's like, I'm okay with being judged on this part, but like I don't want to be 100% vulnerability myself or put too many of like who I am out there for the judgment or if I, you know, maybe if I see it in the wrong way and it hits someone in the wrong way. And then I'm like, oh, that represents Taylor. And it's like every time I go up with him, I'm like more conscious of what I look like. I noticed that where I'm like, oh, like, is this good enough? And he's like, I don't care. He's like, what do you mean? But to me, I'm like, well, like I'm Taylor LeWon's wife. Like that has to be like, that's somebody. You know what I mean? And I think the way that I've channeled it is I really try to give back as much as I can because then I feel worthy of being where I'm at. You know what I mean? Like that's almost like, I think everyone has a different way of coping with it.  How am I going to cope with almost this anxiousness of like the pressure? And I'm like, well, I'll just, I'll keep giving back. I'll keep trying to take care of the community that took care of us. We wouldn't be here without the city of Nashville. And so like I really take that seriously. And so I'm like, how can I help the city of Nashville? Because I'm not going to just turn my back on now that we've made it somewhere in our own individual lives. Like, you know what I mean? Like I don't want to forget about how we got here. And I think that's like kind of my way of saying thank you and it releases some of that pressure from myself. Maybe I always think about that. And I think the closer I get to 30, the more the pressure goes away. It does. I'll tell you whenever, so I was 22 whenever I married John. Oh, wow. And that's the year that he started his career with the NFL. And I felt that pressure. And it wasn't until probably about 10 years later, I think I was actually 29 when we moved to Boston. He was always with the Patriots, but until he got like, he was the director of college scouting. We had to move up there. And I remember being around the players' wives and getting very nervous, thinking that I had to look a certain way or I had to act a certain way. And it wasn't until, and honestly, even when we got this job, it was the same thing. Because now I'm like, oh no. It finally got to the point of, oh my gosh, I'm really 44 years old. Yeah. Just be myself. I don't want to just be myself. And what number is that? You know, from what that glass of wine, who cares if you put a pound or two on me? I don't care. I want to be happy. I think the more comfortable you get in stuff like that, you're also like, oh, people are so worried about themselves that they're not even paying attention to me the way I think they're paying attention to me. You know what I mean? Like it's like, they're all in their own head. But in my, for some reason, I made up this whole story that like, oh, they're thinking this of me and this of me and that of me. And half the time, they're worried about their own stuff and I'm just a blip on the radar. You know what I mean? And that kind of helped free that up for myself as well. But yeah, well, I remember coming into the NFL Wives. I was like, uh-oh. I was like, that was the most nerve-wracking thing I think about becoming an NFL wife. Because I remember when I first came in, there was like, I don't know if you felt this, but when I first came in, there was like this hierarchy. And I was like, oh, I don't want to play this game. Yeah, because of you. So I was by myself a lot. Like I remember there were some years where like, I'd be by myself and I'd turn around, there'd just be a whole row of wives. And I was just like, ah, no, don't I? So I would just sit there and then eventually as the years went on, then I got the invite and I'm like, well, I don't want the invite. It's not something I want to earn, you know what I mean? Like it's like, I want to meet true friendships or whatever it could be. And so like I stayed strong and then it was lonely. And like I'm sure that some girls maybe thought I was being like, right. I don't want to sit with you. But it was protection for myself more than anything. You know what I mean? And now it's like, I have some good girlfriends on the team and I'm super kind and more cordial. I know more of them now, actually, to be honest with you, but it's changed over time. When I first got into it, it was like, oh, I thought high school was over. Like, let me tell you, it doesn't even stop in their 40s. It doesn't stop. It's hard. Yeah, it's hard. It's five and she's already dealing with me and girls. Yeah, crazy. Yeah, she's like, I love myself. This girl said that I was wearing, wasn't nice. I'm like, what? I don't know. Yeah. Where does she live? Yeah, it's her mom's name. Did you figure that out yet? Yeah.  My animal's more than mine. Yeah. Yeah, it does give me, keeps my feet on the ground. You know what I mean? When you're taking care of things and stuff like that all day, it kind of keeps your feet on the ground. But I was a yoga instructor before this. It's kind of what I did when I got out of school because I thought I was going to go into a trade more than spend all the money on doing something I didn't know what I wanted to do one day. Honestly, this is probably my first year. I've been telling everybody this was my yes year because I felt like every time the season would hit, I found myself just waiting for Taylor to get home to make sure like, hey, are you injured?   You know what I mean? And I felt like there was no reason for it because he would say he's like, oh, he's like, what am I? What are you waiting for? Like go do your own thing. And for some reason that wasn't something that clicked in me until like this past year. And I'm like, I'm going to start saying yes more. And it's like, because eventually I'm like, man, I'm just getting miserable and I don't want to resent him one day because he never asked for that. But like, I just feel like, and you could probably relate with it. I do it all the time. You do it, yeah. I do it all the time. Yeah, yeah. It's just something. It's a hundred percent right. Like it's like, you just every minute you can get with him, you want to get. But then I'm getting, I'm getting wore out. You know what I mean? Cause I just feel like I'm like, I'm just waiting.  I'm like, you're going to go to bed at seven. Go to bed at eight. And then you can spend an hour with me. But you know what I mean? It's like, he just wants to get everything he can to this career because it's not forever. And he's closer to the end of the career more than the beginning of his career. You know what I mean? So he just came back from his injury. And if you think that boy ain't going to be serious now, like, oh, man. So it's like he's given everything he's got because in his mind, especially cause he had unfortunate events after he got his second deal. And now he's like, no, I'm earning this thing. And a lot of it, all of it was out of his control. So now he's like, so wants to make sure that he proves himself now. You know what I mean? Just because he couldn't before, he's like, no, I'm here. And even last year, coming back from an injury, I never knew what it took to come back from an injury. And that was one of the most mentally, spiritually, and physically exhausting rollercoaster I've ever been on in my life. Let's talk about when he got that concussion. Where were you and were you from? I mean, I know I was freaking out. I was like that when he was out for three minutes. Yes. Yeah. I was in our suite. And you know, Will, he does his podcast with Will. So Will was with us. And me and Will were standing at the edge. And I was looking around. I'm like, oh, it looks like somebody's injured. And I always scan the field because only him and AJ Brown had red cleats on the offense. So I'd always scan the cleats. And that's how I'd find Taylor, because it's easy to tell the difference between them, one big human and one lesser of a big human. So I would always look around. I'm like, OK, there's AJ. And then I see this group of people. I just see two red cleats sticking out. And they weren't just sticking out. They were like limp. They were like this. And so I was like, OK, what's happening? And so I'm looking at Will. I'm like, what do you think is happening to him? Do you think like, is he knocked out? He looks like he's knocked out because his feet are limp. And Will's looking at me at first. And he goes, yeah, he's probably knocked out. Probably wake up, blah, blah. And then one minute goes by. And I'm like, OK, he's not moving. He's not flinched a foot. He's not. Nothing's happened. No one's letting anybody see anything. I'm like, Will, what's going on? And now Will won't look at me. And he's like, they won't let him move because if it's a spinal injury or something like that, he's not allowed moving. I'm like, OK. Another minute goes by. And I'm like, OK, Will, if he's passed out and it's been three minutes, I'm googling when does brain damage happen? Like, is he dead? Is he paralyzed? Is he? And then minute three came by. And I am shaking. I'm trying so hard because I'm with all these people. Were you with the girls? No. Oh, thank goodness. Oh, that's good. No, it was a late game. Remember, so they were sleeping. Yeah, it was a night game. So they were at home sleeping. And he got pulled off the stretcher. And I could not look up. I was just like, I'm thinking like, none of this was worth it. Like, I was just like, we're fools. Well, how did we do this? Like, I'm just thinking like, now my poor girl is like, I could cry thinking about it. And then he put his thumbs up. And then I'm like, OK, so he's coherent, but is he paralyzed? Because that's still not, he's strapped. Like, he can't move. He just did this. And now I turn around once I saw the thumbs up, water works.  I'm not a very emotional person. I don't really wear my emotions. I'm pretty content in life.  Like, how do we, some people don't want to look at me. Some people are surrounding me. And then Derek Henry and Kevin Byer's wife came in. Maybe more, I don't know. I think Quentin Spain's girlfriend happened to be in town, OK, you know, OK. She, I think she happened to be in town. There could have been more there. So if I forget, I'm sorry. But they come around and they were, I'm in this prayer circle and I'm just crying. Just like, and I just want to be like, I'm so thankful for you guys. But if I don't get to him in the next two seconds, you're going to see a different side of me. You know what I mean? Like, I'm like, I'm about to climb over this edge. I'm climbing. I want to climb over seats and get to the field. Like, I'm about to be hauling a variable. Like, you get my down on the field right now. You know what I mean? Like, I'm like, if I was, I'm thankful I was in this week because if I wasn't in this week, you would have been out there. I would have been security escorted out of that stadium because I was getting on that field. Like, I'm like, I don't care about any of this anymore. Like, I'm getting to my husband. Yeah. And when it's so traumatic in these times, you don't remember every detail. Absolutely not. So I'm coming down. I'm staring at the ground. I don't want to see fans. I don't want to see anything. I'm just staring at the ground because I've got the 77 jersey on. I just don't want to see anything.  Apologizing?   You cry every episode. So, oh my gosh, David. Yeah, he said, he's super apologetic. And I said that. Thank you so much, but you're done. Yeah, we're done with this. I'm like, you're never stepping on that field again. I looked at variables like, thank you so much. But we're done. I'm like, we're done. This is it. It's over. I love you to great career. But you know, let's go home now. Like, this is like, you're getting in my car and we're leaving. I can't even like, that's what I can say. And I remember Mitch the faster was like, this is probably not the time. I looked at Mitch and I said, this is exactly the time. I was like, I was not to be.  Yeah, I'm like, no. I am on this one. So he was like, I'm OK. I promise. Like it's like in the doctor and everybody's talking to me. So we went and got a CT scan and everything came back surprisingly, like perfect. Like, but you know, you never know until. Right, so scary. It's so scary. Oh my gosh. Oh my gosh. So yeah, that was, that's another tough part of being an FL life is, you know, there's nothing, there's nothing worse than that few seconds where you're like, oh, we're going to be that 1% of the 1% and this is going to, our lives are forever changed. I bet after that now. I mean, I'm sure before that you were always nervous during the game. I bet it's a whole new level. I can't look at him. Like before I only used to watch him play. Like, I didn't know where the ball was. I didn't, I was just making sure he hit everyone. So after we could talk about which play and I was like, could you do that? And like, oh yeah, he kind of missed a step here. And what was that all about? Like we talk about, now I'm like, I don't know what you did. I'm not looking at you. Like, I cannot look at him. I have to stare at the ball. At every snap I ask myself, is Tana Hill going to throw it or run it? And that's how I distract myself from looking at him. Like I just have to, I try to guess if he's going to throw it or run it. And then that's it. And I'll follow the ball. Like I can't look at him. Oh my God. Oh my God. It's too much for me. So scary. I had to tell you my most favorite Taylor story. They had a fight on the field and I was like, percing my mind, where's Taylor? Yeah. Oh, I know. Where's Taylor? And then I look and Taylor's all the way on the other side of the field sitting on the, sitting on the field. Yeah. So that way he doesn't get up. He doesn't get up. So Taylor had a year where he had so many penalties. Oh no. For Halloween he dressed up like a yellow flag. Like he had that many penalties.  Like just like stay out of it. You don't need to be involved in everything. And so when he did that, I'm like, use some more. He like sat on his pants like a little. He was sat there like this and he was like, this is so fun. There's a picture of it online. I see. That's hilarious. That was hilarious. Oh, that's amazing. Let's talk about feeding Nashville. Okay, yeah. And tell the audience what it is and how you and I was Haley Hubbard. Yeah. Had started it. Let's talk about that. So there's this like group chat of women and it's like wise or artists of just people around Nashville that just have a really empathetic heart to help. And we always get in there and whether it's like their neighbor needs help or like we have some idea we want to start or someone's throwing an event of some sort. We all put in this group chat. And so Nashville got hit with a tornado and then like a month later got hit with COVID and this community just got destroyed. Right. And so I went in the group chat and said, Hey, I have an idea. And I was like, we have all these because in this such a, you know, culinary experience in Nashville there's so many restaurants here. So I'm like, we've got a lot of restaurants of chefs and employees being for load. And a lot of people are going hungry because they had promising jobs and now they're gone without, you know being able to predict that. So I said, what if we raise money to pay chefs to create food to give to whoever wanted it? Like nothing to prove. I don't want to see no stamp or income or just anybody who felt hungry can come get it. And then Haley side texted me and she goes, I'm in. Let's do it. Like how can we do this? And then she took off. She found someone in San Francisco who's kind of doing the same thing. We went back and forth with them and they're a dream. They helped us like kind of figure out how they went about it. And then we kind of took some of that template and like made minor changes to make it work here. And then we took Ryan from place map and he started running the kitchen because he does this like in house catering. So like he brings a restaurant to you. So like if you want to have a dinner guest like he'll come and cook you a beautiful meal and clean it and go. And so he helped me find all these chefs and kind of run this kitchen out of citizens kitchen. And then I think like as of like six months ago I think we were at like 76,000 people we've fed. That's amazing. Yeah. So like it just kind of went on from there. And now Ryan really heads the thing. Haley and I kind of passed the reigns and we still helped raise the donations. But like he's true. I mean he's a heartbeat of the thing. It should have been his name on it from the beginning. But yeah. So he runs it pretty much full time and he's kind of taking it under place mats wing as their charity. That's amazing. Yeah. They're taking off. See it's really hard to be an NFL life. But it's things like this whenever you have a passion and whenever you take your platform and use it for good. Yeah. You know. I mean with your animals with helping the homeless. And it's just it's amazing and kudos to you. Oh thank you. It gives me self purpose. It separates me from like you know all football world and all that. So it gives me just makes me feel like I'm doing something. Yeah. There's something other than Taylor's wife. Even with doing like podcasts and stuff I think even if you would have asked me to come on here a year or two years ago I would have said no.  You know what I mean. Like I feel like you're especially in your 20s like you're just you're trying to figure yourself out. You know what I mean. And it's like to put yourself out there in the midst of this like phase of your life of trying to educate and learn yourself. And then you know if you take scrutiny on some level of that it's like you're so vulnerable in that phase that like if you're not sure about yourself it's easy to get knocked on your butt. And I think that going through that with Taylor and stuff like that I was like oh I got to figure out where my shoes are. You know what I mean. And like because then I can be more sure of myself and then like come out on something like this and like be able to experience this and kind of you know have my feet in the ground. Well I also think with having little kids I mean I have an 18 month old and a seven year old you're like it's hard to even know like right from left like you're just changing diapers and feeding people and you're like why do you have to eat so much and like you have 400 snacks a day and like I can't and so it's like it's hard to even focus on yourself.  Yeah you know being here with no family or anything I was pretty much knee deep in kids 24 seven. Yeah. But then we recently got when I had my second we got a full-time nanny. That's nice. I love her so much. You have to. You have to have people that can. Yeah. Oh my gosh even just being able to be home and having an extra set of hands. You know what I mean. And it takes a pressure off of when Taylor comes home and I'm like here. Yes. You know what I mean. Like take home. Let me breathe.  Reconnect. Yeah. And it's just like it's just so important and I think for a while I felt so guilty because I'm like I'm a stay at home mom I should just be doing this all by myself. And then I'm like who can do this by themselves. Single moms that's going to be my next thing is I really want to focus on single moms and foster moms because I just have the utmost respect for how they do it because there's no way you don't lose yourself in it. Yeah. You know what I mean. Like it's like and I just want to extend a hand because I think in our society we have really isolated moms to think that like you have to do it all by yourself. And then if you go into other cultures it's a community thing. Yeah. And everyone's raising these kids. It's never just mom. In some communities after the mom has baby they're only allowed feeding them and that's it. And everyone takes care of them, gives her mud baths, wraps her in things for all this healing and like oh my gosh. I know. I'm in the wrong place. I feel like we've really lost the sense of community in our society. I was talking about that like we used to know who our police officers were, our teachers were, all of the above and now I don't know anybody. I don't even know my neighbors. And you know being in this lifestyle I feel like you sometimes put walls up because you're like why do you want to be my friend? Why are you talking to me? You know what I mean? So I'm trying to find this like line of like how do you bring me back? And it's hard to ask for help as it is for females. You know it's like we want to do it all and I think there was that culture for so long like if you're not perfect like you're failing or something and now I think the walls are falling down where we're like I need help. Like I'm drowning. I guess what we were never perfect. Yeah like I'm never gonna be perfect and get over here and drink glass of wine with me before. I lose my mind. I think a lot of people think that if you say like hey I'm not doing okay. It's like oh I'm failing. But it's like no I'm just not doing okay. I mean it's like I don't think I think everybody has those moments. Have you found a good group of moms here that you can kind of have that? Probably like you know they always say like the first group of friends you have in a new town will never be the friends you end up with. Which I like I still am like close with them but I like really reconnecting the last year with this really awesome group of moms. And so like we've really enjoyed it. My girls are getting, my girlfriend especially is getting true friendships now. Like she's got this one friend that I swear she would take a bullet for. Like I have, it is so, it's I'm almost like it's like, like she's addicted to her. Like I need to see her 24 seven. Like I'm just like what? Yeah. And like she at school, she was supposed to draw like the woman who inspires her and she drew her. Oh my gosh. Oh my gosh. Okay. Okay. Okay. So funny. I guess I won't be offended. That's hilarious. She wrote, oh, who is this? She goes Olivia and I was like, oh, that's so sweet. That's awesome. So funny. Yeah. You end up like having to have those friends do when your child is addicted to someone. You're like, okay, I guess we're hanging out all the time. Exactly. Like her mom and I are friends. It's Haley's daughter. Oh, nice. Yeah. Luckily we get to hang out and they get to hang out. So it worked out in my way. That's so good. Sony, because when we lived in Boston, that was cause I'm from New Orleans. So I was really far away from home and I didn't have like family or whatever and my girls were really young. And I still to this day, that group of women are still my best friends. There was five or six of us and we all came together because of our girls. And you just need that. You need to depend on them. It's so important. Luckily all of my houses on my street are like this far apart, like 10 feet. Whatever the legal code is. And it's all kids and all moms that are amazing. And so it's just like, hey, your kid's in my house now. Like let me know when you want them home or whatever, can she mac and cheese? Like we've got extra, so it's fun. When I was back home this summer, I've had one of my best friends since we were like 14. She's got a daughter and I've got two and she's pregnant with her second. But it was fun because like we got to do the things that are boring together.  If our kids were driving us nuts, we'd just all throw them into one pit together. You know what I mean?  And we're just with each other and it's like, gosh, this is so much more fun now that I have someone to do it with. You know what I mean? It's like, I think people forget how important friendships like that are. And everyone always focuses on like their relationship with their spouse. But it's like, it's so enriching for your soul to have that friend that like, even if it's one that like just shows up at your house or like if you're in a bind, we'll come pick up your kids for you. Or like, you know what I mean? Like it's like that I feel like I missed out the most in the years that I was here and I was so dedicated to being a wife and a mom. And I was like, something's missing. Like I'm not, I don't feel fulfilled. And then also when I went and hung out with her, I'm like, oh my God, that's what's missing. That's amazing. I know that's one of the hardest things about not living in my hometown. He never wanna complain, you know what I mean?  Like it's like even not being in your hometown, especially if you like being in your hometown, you have like good roots there. You miss out on so much. Like it's like, I went back there and I'm looking around and I'm like, wow, everyone's gotten older. Like, you know what I mean? Like you and my grandparent, no one froze while I was gone. Like that was the deal. You know what I mean? Like I feel like you guys just wait and I'll come back and then you guys can live. But like, it's like they just lived all this life without you and it's like, so there are these little sacrifices you have to make, but I think to hear you that it goes on to like your whole life. I'm like, oh my God, I gotta get back home. Oh my God. Seriously, I do. I still, I think about it. Y'all, the most incredible thing happened yesterday. I was at one of the hotels here and my girlfriends and I walked up to the rooftop and all of a sudden I see this person from afar looking at me and I'm looking, I kept looking at him and I'm like, how do I know that person? And I'm thinking, of course I'm thinking Titan stuff and you know, I met him through John or whatever. And next thing I know, he's standing right next to me and he goes, Jamie? And I was like, yeah. Y'all, it was a friend of mine from back home. I actually was friends with his brother. I actually dated his brother. But, and him and his wife were here working for the Grand Prix like doing something with that. Oh cool. It was the craziest thing. So they got to meet all my friends and it was, it was just, I mean, that was the best thing of my night. And I'm like, I never see anybody from back home. It just warmed my heart. That's awesome. That's so special. Yeah, I loved it. I grew up here so I get that experience like once a week.  House life. Do you have friends from like high school still today? I do, yeah, yeah. It is, it's fun. I mean, it's like, it can be overwhelming because you're kind of expected to keep up with so many relationships and like I want to, you know.  And so it's kind of hard to manage, but it's also awesome. I think that is hard. Yeah. Well, you're so amazing. We've like loved talking to you and happy. What is this, Taylor's, how many seasons is he in now at the Titans? Jamie, you know how nine? This is our seventh and he was here before. Yeah, I think 2014. Oh, wow. Okay, yeah. Ninth season, that's crazy. He, I have to say, one of my favorite stories about John, I have a bunch. Yes, tell us. And Taylor loves John, just so I know. Taylor loves John. Like I think Taylor sometimes wished that John was on his boss so he could hang out with John more. Like I really do believe that.  Like he always makes sure he gets into every detail and he's talking about John. It's so funny. But when we were going through all this stuff with Taylor and I'm thinking like, oh, the team's gonna turn. Like they're not gonna believe them, blah, blah and all this stuff. And John made his way out to me. Like, it's not like John and I talk. So John came up to me and he goes, hey, how are you? Like how are you doing? And I'm like, I don't know how to feel. Like I wanna just take this all away from Taylor. He goes, just so you know, like we know you. Like we know when we trust you. He goes, and I'm so sorry this is happening to you.  And I was like, how many? That's amazing. Teams would go out of their way. Like how many GMs would go out of their way to make sure I knew that like, you know, my husband was stood behind? Yeah. You know, and I think that's why Taylor literally wants to run through a brick wall for him. He really does. But I just remember like that always stuck with me. And I just was like, I've always, anytime people ask about the Titans and the associations, stuff like that's always a story I told. Because I just felt like it just was such a big moment. He is so passionate for the players and for the team and for the grass.  He's extremely passionate. Oh, it's super easy to see. Well, I laugh at them because the other day we were at practice and my John was talking and all of a sudden here comes Taylor. It's like the big old guy smacks John. He messes with John so much. I mean, variable two though, I feel like they're just all cut from the same cloth. Those three, they really are like in them all in a room. Like variable and Taylor just remind me so much of each other. It's not even funny. Like I feel like they're just like generations apart but they're like the same person. And then John comes in and you can tell John has to be a little bit more serious but like you can tell that like he eats it up. You know what I mean? Like he lets a little smirk out and then it's over. Taylor, if Taylor sees one little smirk it's game over. Now everything's okay. I love it. I love it. I think he's so much for doing this. Of course. Yeah, I have so much fun.


Our story has been written and it was written earlier today when Tom Brady said that he was done in New England very strangely the the headline on the story was a Patriot Forever But obviously not right now. So as we go, this is and Tom Brady is Is going to sign somewhere else that will not be with the New England Patriots And I will tell you my initial thought and I think I will come under some fire by both Don and Peter Before I give you it, I'll tell you this Under no circumstances do I say he does not have this right. He has the right to go wherever he wants He's played 20 years with New England. There's the first time he's chosen to be a free agent. So he has the right to go somewhere That's not my point. My point is why because wherever he goes whether it be L.A. Chargers Oakland rate the Las Vegas Raiders The Miami Dolphins of the Tampa Bay Bucks in the next two years those teams are not winning a Super Bowl period They're not so what's the point?  Is he so suffocating that you had to get out? I don't understand it. It doesn't make sense to me and unless he could somehow articulate it because what he sent out on Instagram today He loves everybody. He loves everybody loves Belichick.  It's the best. He's a patriot for life. Then what do you leave him for? What's it? What's the big what's the big kick for I don't get it It makes no sense to me jet fans are thrilled today Bill's fans are thrilled today dolphin fans are thrilled today. I get it I just don't understand the urgency to leave a perfect situation because you could say Well, they're not when they're not built to win a Super Bowl. Well, they made the playoffs last year They're not built to win a Super Bowl you tell me the other three teams the other three coaches that he might be going to None of them none of them could sniff Bill Belichick. I still take my I love I love people are going Oh, the bills are now the favorite in the East.  No, no He's gonna put together a great team make the playoffs again Probably not win a Super Bowl, but he's got something to prove as well. Why is Tom Brady leaving? I don't understand nobody's been able to articulate it for me Well, I think I can Michael and again I'm trying to get into his head the same way you're trying to get into his head and eventually He'll have a press conference or write a book to articulate the exact reasons why and I don't think it has to be contentious I don't think he has any hatred towards New England I completely believe him when he says that he loves everybody over there But this the difference between Tom Brady and every other great athlete I can think of I've been racking my brain all day Michael There is not another great athlete That I believe in the history of sports any sport you want to name That is more attached to the coach than Tom Brady is Even Jordan who didn't win a thing before Phil Jackson got to Chicago, right? Jordan was what? 27 when he won his first championship with Phil. It's a long time of the NBA before he won his championship Nobody ever says it says Jordan and Jackson never it's not it's not a phrase It's it's a phrase in the NFL. It's a it's a it's a sports Combination Bella check Brady Brady Bella check they've been connected Tom Brady's entire Career Tom Brady has done nothing in the NFL that wasn't attached to Bill Bella check Bella check went 11 and five with Matt Castle was a Hall of Fame defensive coordinator It's still the only head coach in Cleveland with the Cleveland Browns So we say that he's the last coach to win a playoff game in Cleveland He's got an extensive resume that's not attached to Tom Brady But Tom Brady everything is Bill Bella check name a player go to you can go to Jim Brown You can go to Lawrence Taylor Lawrence Taylor isn't attached to Bill Parcells He spent most of his career at Bill Parcells not attached Wayne Gretzky's not attached to Glenn Sather Dan Marino Don Shuler Is it a thing? Because they didn't win a championship, but I don't think it's a I don't it's it's not a thing either way It's not a lot of thing But Bella check Brady Brady Bella check is a thing and I think he's got the opportunity now The window is beginning to close where he can go and kind of prove to the world that he is a great quarterback and do Something that's not attached to Bill and that doesn't mean he hates him Doesn't mean that it's contentious But it just means I just want to prove to the world that I can go to Tampa or I can go to Los Angeles And even taking those teams to the playoffs Can look like an accomplishment because staying into England and compiling championships is still compiling the myth The enigma that is Brady Bella check and I think he just wants to break that combination I I think I think Don makes a lot of interesting points and I would add to that That there's also the possibility that he is aware that his abilities are down a tick And that with the kind of talent they tend to surround him with and particularly they surrounded him with last year He just knows it's going to be ugly again in new england And he'd rather go someplace where he's able to have maybe more weapons and have a lower bar Because in new england no weapons right now no great weapons and also the bar is super bowl So why not go someplace where you might have new weapons and the bar to Don's point is just make the playoffs But but peter can you honestly say all the teams that are supposedly in play for him right now That even with tom brady. Are they going to be better than new england? No, they're not I they're not I think the raiders would with brady would be better I I would bet you any first of all it can't be the raiders They just signed mariotta. They have car as well. That's a good point Unless they're going to hold on to mariotta mariotta and then and then No, you're right brady and get rid of get rid of car. I just the dolphins aren't ready to win Tampa Bay has great receivers. They're not ready to win They don't have a defense that's going to win But it's the whole thing of taking something. It's not ready made And to go out there. So you you're willing to You you drive a lamborghini you want to build your own car you build a rambler But you feel better because you built the rambler rather than buy the lamborghini It doesn't make sense What's he trying to get out of it unless he wins a super ball somewhere But you the only thing that would make sense to me don is if he goes to the cowboys They got a chance to win a super ball that would make sense But I think you're underestimating just the freedom of now being able to try the challenge of accomplishing something that That he can actually get credit for The only thing he's going to get credit for is going to the plus. He's not winning a super ball But let's look at bill bellichick as I mentioned like we praise when we get into the debate like the debate always is Who needs who more and we always kind of fall on brady needing bellichick because bellichick was able to go 11 In five with matt castle. He didn't make the playoffs that year But he went 11 and five He won a playoff game one lousy playoff game in cleveland, but that's that's something that he accomplished without tom brady If tom brady can go to la and sneak him in as a wild card If he can go to tampa and go nine and seven He can kind of create a resume of that's a heck of a quarterback That he was able to go to tampa and actually make them relevant and get them into the playoffs You know what challenge for it


In the last lecture, I introduced the concept of testing of hypothesis. We saw that Neyman Pearson approach in which they consider the probabilities of type 1 error and type 2 error and based on that the test procedures are devised in which we concede we put a restriction on one type of error usually the type 1 error and we call it the size of the test and subject to the tests functions satisfying the size of the test condition we find out those tests which have the maximum power. So, they are called most powerful test as some solution was proposed for simple versus simple hypothesis cases and later on these procedures were extended to the case of composite hypothesis also certain type of composite hypothesis and then for certain type of composite hypothesis uniformly most powerful and biased tests were also devised. In place of giving the full details of the derivation of the test I will be basically explaining to you the procedures that the test that have been obtained using this and how to use them. So, let us consider testing for the parameters of normal populations. So, let us consider say x 1, x 2, x n following normal mu sigma square distribution we consider testing for mu. Now, let us consider say case 1 when sigma square is known now we consider various kind of hypothesis we consider say first problem I will call the hypothesis testing problems as h 1 k 1. So, h 1 mu is equal to say mu is less than or equal to mu naught against say k 1 mu is greater than mu naught. In this particular case we consider x bar that is following normal mu sigma square by n. So, we consider root n x bar minus mu by sigma that follows normal 0 1. So, we consider the test statistic z is equal to root n x bar minus mu by mu naught by sigma. So, if you consider if I consider this as z alpha then this probability is alpha. So, if we consider probability of z greater than z alpha that is equal to alpha and here we are considering mu is equal to mu naught. So, the uniformly most powerful test of size alpha for testing h 1 against k 1 is reject h 1 when z is greater than z alpha where z is given by root n x bar minus mu naught by sigma. Actually it can be shown that it can be shown that if I consider probability z greater than z alpha then the supremum of mu less than or equal to mu naught is attained at mu is equal to mu naught. Therefore, this is the most powerful test of size alpha. So, of course, since this is composite hypothesis situation we will say it is the uniformly most powerful test here. Now, we have the variations in place of h 1 that is mu less than or equal to mu naught if we take h 1 star that is say mu is equal to mu naught versus k 1 mu greater than mu naught then also the same test procedure will be applicable. Now, the main reason is that actually since here the maximization is occurring at mu is equal to mu naught. Therefore, when the null hypothesis is true mu is equal to mu naught will be coming here and in this case the maximum is occurring at that point and the power is decided by the alternative. Therefore, the test function will not change and the test procedure will also not change. So, you will say accept h 1 if z is less than or equal to z alpha here equal to z alpha has no significance because the probability that z is equal to z alpha will be 0 because z is a continuous random variable. Now, naturally one may think that in what happens if we change the null and alternative hypothesis. For example, here alpha is the probability of maximum probability of type 1 error that means, we are rejecting and the null hypothesis is true. Now, if that is considered to be more serious for the beta in that case we may like to interchange the hypothesis and we may consider. So, let me call it say h 2 mu is greater than or equal to mu naught against k 2 say mu is less than mu naught. I have interchanged the role of null and alternative hypothesis, but the equality I have included in the null hypothesis. So, in this case we will be considering the rejection on the left side because you will be considering here. So, you will consider reject h 2 if z is less than or equal to minus z alpha and of course, accept otherwise accept h 2 otherwise. See in this case this hypothesis is also equivalently we may test h 2 star mu is equal to mu naught against k 2 mu is less than mu naught. Basically once again if we are considering this one then the probability of say z less than or equal to minus z alpha when mu is equal to mu naught that will be alpha and when we are considering for a general mu in this region then the maximum value will be attained when mu is equal to mu naught and therefore, the size will be alpha. So, this is the uniformly most powerful test of size alpha. Now there may be situations where we may not like to test greater than or less than rather whether a value is equal or not. In that case we formulate the hypothesis testing problem in the following fashion. We consider say h 3 mu is equal to mu naught against k 3 mu is not equal to mu naught. Now naturally in this case the rejection region will be on both the sides. So, we consider say z alpha by 2 and minus z alpha by 2. So, you will consider actually this is uniformly most powerful uniformly most powerful unbiased test of size alpha. So, that is reject h 3 if modulus of z is greater than z alpha by 2 where z is the same quantity that is z is equal to your root n x bar minus mu naught by sigma. So, you are rejecting in this region and in this region and in the intermediate region you are in favor of the hypothesis except h 3 otherwise. Now in case sigma square is unknown then naturally this z cannot be used. If you remember the development of the confidence interval there in place of sigma we had used s there where s square was 1 by n minus 1 sigma x i minus x bar square that is the sample variance. So, we consider the situation sigma square is unknown then consider s square that is equal to 1 by n minus 1 sigma x i minus x bar square. So, we consider say t that is equal to root n x bar minus mu naught divided by s. So, if we consider say root n x bar minus mu by s then that follows t distribution on n minus 1 degrees of freedom as we have seen in the confidence interval problem. So, if we consider this mu replaced by mu naught then the test statistic will be following the t distribution and we can consider the problems. So, for h 1 mu less than or equal to mu naught against say k 1 mu is greater than mu naught then we will have the test as reject h 1 if t is greater than t n minus 1 alpha. If we consider mu is greater than mu naught against k 2 mu is less than or equal to mu naught then the test will be reject h 2 if t is less than t n minus 1 1 minus alpha that is minus t n minus 1 alpha because of the symmetry. Then the third situation comes for the two-sided test that is for mu is equal to mu naught against mu is not equal to mu naught then we will consider reject h 3 if modulus of t is greater than or equal to t n minus 1 alpha by 2. So, you will have a two-sided rejection region here this is alpha by 2 and this is alpha by 2. So, these are the most powerful unbiased test for the size alpha for these problems here. Now, one may like to test for the variance also. So, if we consider the test for the variance testing for sigma square then again you will have two cases one case will be when mu is known. If mu is known then we can consider sigma x i minus mu square by sigma naught square. So, if we consider this as w then this is following chi square distribution on n minus 1 degrees of freedom when sigma square is equal to sigma naught square. So, if we consider the hypothesis testing problems based on this. So, for example, let us consider say sigma square less than or equal to sigma naught square against say sigma square is greater than sigma naught square then we will consider the rejection region as reject h 1 if w is greater than chi square n minus 1 alpha because chi square is a skewed distribution and we will have this situation here chi square n minus 1 alpha. So, this probability is simply alpha. As I mentioned earlier we can also consider sigma square is equal to sigma naught square and here sigma square greater than sigma naught square is still the test function and the test region will be same. And we may consider reverse situation sigma square greater than or equal to sigma naught square against k 2 sigma square less than sigma naught square then the test procedure will be reject h 2 if w is less than chi square n minus 1 1 minus alpha this probability is alpha. So, this is not a symmetric distribution therefore, we cannot write minus here and we will have a two sided region if we consider sigma square is equal to sigma naught square against sigma square is not equal to sigma naught square. So, the test procedure will be reject h 3 if w is less than chi square n minus 1 1 minus alpha by 2 r w is greater than chi square n minus 1 alpha by 2. So, this will be most powerful test uniformly most powerful test of size alpha here in the case 1 and 2 and in the case 3 it will be uniformly most powerful unbiased test for of size alpha here. Now in the case when mu is unknown then we base our decisions on let us call it w star that is n minus 1 s square by sigma naught square. So, that follows chi square distribution actually I made a mistake here this should be n here because this is following n this will be n this will be n these are will be n degrees of freedom. When mu is unknown then you will have n minus 1 degrees of freedom and then the test procedures will be for first case reject h 1 if in the second case it will be reject h 2 if w star is less than and in the third case reject h 3 if w star is less than chi square n minus 1 1 minus alpha by 2 r w star is greater than chi square n minus 1 minus alpha by 2. This is about the testing for the parameters of a one normal population. Now this type of methods have been can be applied actually to other distributions also in which certain nice properties for example if the distributions are in the exponential family if the distributions are having monoton likelihood ratio even though they may not been the exponential family in all those situations this type of testing procedures are applicable. Now I will briefly touch upon the two parameter two population model for the normal populations. So, we consider two sample problems like in the case of confidence intervals we have two samples available to us. One is from say a normal distribution with mean mu 1 and variance sigma 1 square and another independent random sample that is available from normal with mean mu 2 and variance sigma 2 square and these two samples are taken independently. Now we consider say parameters mu 1 mu 2 sigma 1 square sigma 2 square these could be our testing problems. Now one of the you can say commonly used problems could be to test whether the mean of the first population is less than the mean of the second population or equal or greater than etcetera that means we are interested in the difference here. Now naturally this is a problem which can be handled easily using the Neyman Pearson theory. So, we consider testing for means if we consider the testing for means we may consider hypothesis problems of the nature say mu 1 less than or equal to mu 2 mu 1 is equal to mu 2 mu 1 greater than or equal to mu 2 and so on. These are the types of hypothesis problems that we may have. So, again as before we consider case one when sigma 1 square and sigma 2 square are known. If sigma 1 square and sigma 2 square are known then we consider the statistic of the form let me call it z star that is equal to x bar minus y bar minus divided by square root sigma 1 square by m plus sigma 2 square by n. Now when mu 1 is equal to mu 2 then z star follows normal 0 1. So, we utilize this actually. In fact, it can be shown that the maximum of the probability of type 1 error will be achieved when mu 1 is equal to mu 2. Let us consider various hypothesis testing problems here. Say mu 1 less than or equal to mu 2 against say mu 1 greater than mu 2. Naturally if in the alternative case we are saying mu 1 is greater than mu 2 that means we will be considering the rejection region on the larger side. So, we will consider here that is z alpha. So, we will consider reject h 1 if z star is greater than z alpha. In the second case here we will be rejecting for the small values of z star. Now if we consider the small values then on the left hand side we can consider z 1 minus alpha which is equal to minus z alpha. So, the rejection region will be reject h 2 if z star is less than minus z alpha. And once again for the two sided problem we may consider see we may consider this as h 2 here. So, this will be h 3 mu 1 is equal to mu 2 against k 3 mu 1 is not equal to mu 2. So, you will consider reject h 3 if modulus of z star is greater than z alpha by 2. That means we will be rejecting on both the sides of the normal curve. That means if the values is in this gene or in this zone that is minus z alpha by 2. Now we consider the second case when sigma square is equal to sigma 2 square is equal to say sigma square, but this is unknown. If this is unknown then we formulate the test statistic. Now let me briefly mention about the large sample cases also. See if we look at the case that I discussed in the beginning here we are considering the approximation by the normal 0 1. Now suppose the original distribution need not be normal, but if we are considering the testing for the mean and we have large sample in that case we can consider by applying central limit theorem that this will be approximately normal 0 1. So, the test procedure that I have mentioned here will still be applicable for the large sample cases. However, when sigma square is unknown in that case this procedure will not be applicable. Similarly, in this problem when I considered comparison of mu 1 mu 2 when sigma 1 square and sigma 2 square are known in that case even if the original populations need not be normal then by central limit theorem this result will be applicable. However, when sigma 1 square sigma 2 square are unknown then this result central limit theorem will not be applicable and we have to go for the exact procedures. So, let us consider here if we remember our notations that we developed for the confidence intervals that is we considered S 1 square is equal to 1 by m minus 1 sigma xi minus x bar square and we considered S 2 square is equal to 1 by n minus 1 sigma y j minus y bar square and S p square was taken as m minus 1 S 1 square plus n minus 1 S 2 square by m plus n minus 2. Then based on this we had considered that when mu 1 is equal to mu 2 then you have x bar minus y bar multiplied by m n by m plus n divided by S p this has t distribution on m plus n minus 2 degrees of freedom. Therefore, we can write down the tests for all the 3 situations and let me just repeat it again we are having the testing problems that is h 1 versus k 1 that is mu 1 less than or equal to mu 2 versus mu 1 greater than mu 2. In this case your rejection region will be on the right hand side that is t m plus n minus 2 alpha. So, your region will be reject h 1 if so let us call this quantity say t 1. So, this is equal to t 1 greater than t m plus n minus 2 alpha. In the second case you will be on the left hand side. So, you will say reject h 2 if t 1 is less than minus t m plus n minus 2 alpha and for the 2 sided case it will be reject h 3 if modulus of t 1 is greater than t m plus n minus 2 alpha by 2. Now, the third case is when sigma 1 square and sigma 2 square are completely unknown. If they are completely unknown in this particular case we consider say t 2 that is equal to x bar minus y bar divided by square root S 1 square by m plus S 2 square by n. When mu 1 is equal to mu 2 then t 2 has approximate t distribution on some p degrees of freedom where p is given by S 1 square by m plus S 2 square by n whole square divided by S 1 to the power 4 by m square into m minus 1 plus S 2 to the power 4 by n square into n minus 1. We usually take p to be integer part of the right hand expression. So, the test procedures can be formulated the test procedures for h 1 versus k 1 h 2 versus k 2 and h 3 versus k 3 can be based on. So, I am not describing here for example, in the first case it will be rejecting h 1 if t 2 is greater than t p alpha. Similarly, in the second case it will be reject h 2 if t 2 is less than minus t p alpha and in the third case it will be reject h 3 if t 2 is modulus of t 2 is greater than t p alpha by 2. We had also considered a case of paired observations. In the confidence interval I had described the situation that is where mu 1 and mu 2 are resulting from the same set of individuals or items. For example, it could be the certain learning procedure and we look at the ability of the candidates before conducting the learning procedure and after conducting the learning procedure after a certain time. For example, you could say x i's are the scores on tests of n students before the coaching you can say and y i's are the scores on tests of n students after the coaching. In this case we can consider say x i y i this is following a bivariate normal distribution with some means say mu 1 mu 2 and variances sigma 1 square sigma 2 square and co variances rho sigma 1 sigma 2. So, if we want to compare mu 1 and mu 2 we may as well consider say d i that is equal to y i minus x i or x i minus y i say. So, then this will follow normal mu 1 minus mu 2 and sigma 1.  Now, it is immaterial we can actually consider our observations to be d i's and we can calculate d bar that is 1 by n sigma d i and we can consider s d square as 1 by n minus 1 sigma d i minus d bar rho square. And we can formulate the test statistic let us call it t 3 that is equal to root n d bar divided by s t. So, the test procedure then for h 1 that is mu 1 less than or equal to mu 2 versus k 1 mu 1 greater than mu 2. Once again you can see here it will be reject h 1 f t 3 is greater than t n minus 1 alpha. Similarly if I consider h 1 mu 1 greater than or equal to mu 2 versus k 2 mu 1 less than mu 2 then it will be reject h 2 f t 3 is less than minus t n minus 1 alpha. Similarly if I consider the two sided testing problem mu 1 is equal to mu 2 against mu 1 not equal to mu 2 then the test procedure will be reject h 3 if modulus of t 3 is greater than t n minus 1 alpha by 2. So, we have considered various cases for the comparison of the means of two normal populations. Let us also consider a case for comparison of the variances of two normal populations comparing variances. So, that means we may have a testing problem of the nature. So, let us write say tau is equal to sigma 2 square by sigma 1 square. So, we may consider say tau is less than or equal to say tau naught against say tau is greater than tau naught tau is greater than tau naught tau is less than tau naught tau is equal to tau naught against tau is not equal to tau naught. In all these cases we may consider say s 2 square by s 1 square let us call it say v. Now when sigma 1 square is equal to sigma 2 square tau will be equal to 1. So, then v will have f distribution on n minus 1 m minus 1 degrees of freedom if tau is equal to 1. Therefore, we can use this for the testing here. In the first case it will be reject h 1 if now you can see here you have to reject for the large values of tau. So, large values of tau will correspond to the large values of v.    Of course, we may also consider the case when mu 1 and mu 2 are known. In that case the only thing is that in place of s 2 square by s 1 square we can consider sigma yj minus mu 2 square divided by sigma xi minus mu 1 square and this f statistic will be replaced by f n m in rather than n minus 1 m minus 1. So, without spending too much time on that I will just skip that portion. So, this is the case for the comparison of the variances. Now, equivalently we may have testing problem for the proportions also testing for proportions. For example, if I am considering say x following binomial n p and we may like to test about say p is equal to p naught or p less than or equal to p naught as before. So, we may consider the tests based on x minus p naught because x by n is the let us write it as p hat that is equal to x by n and q hat is equal to 1 minus p hat. So, we may consider basing our tests on this. We can consider p hat minus p naught divided by root p naught q naught by n and we can consider the normal t for this thing that is when p is equal to p naught then this is approximately normal 0 1. This is approximation for n large. So, we can let us write it say some z 1. So, we can base our tests on z 1 for hypothesis h 1 versus k 1 or similarly we can consider p greater than p naught against p less than or equal to p naught etcetera all those kinds of cases can be considered. We can also consider this situation x following say binomial m p 1 and y following binomial n p 2 and we may like to compare p 1 less than or equal to p 2 p 1 greater than p 2 etcetera. So, we can consider base on the differences x minus y and then we can consider the p 1 q 1 by etcetera. So, all those things can be done. I am not spending too much time on this problem here. Now, the test that I have discussed here they are based on the Neyman Pearson theory. However, there was another approach which was considered by R A Fisher and others that is based on the likelihood ratio. In fact, Neyman Pearson came to the f 1 by f naught form based on the likelihood ratios only. However, the approach in a more general form can be described like this. So, let me mention this thing likelihood ratio tests. Let us consider say x 1, x 2, x n be a random sample from a population with some distribution. So, it could be say f x theta we just write in general. Here theta belongs to some parameter space theta. We want to test h naught theta belongs to say omega naught. Let me just change the notation here. This omega let me write here. So, this omega naught is a subset of omega. As you have seen in all these problems like in the binomial problem p was lying between 0 to 1. So, the parameter space was 0 to 1, but in the null hypothesis we are restricting attention to 0 to p naught. If you consider the previous problems of normal populations etcetera for example, here you are writing sigma square is equal to sigma naught square, but here your mu range is from minus infinity to infinity and sigma square can be greater than 0. So, full parameter space is that, but in the null hypothesis you are saying mu is equal to mu is from minus infinity to infinity, but sigma square is equal to sigma naught square. So, you are specifying a region. In the Neyman Pearson theory it was essential to specify an alternative hypothesis, but in the case of likelihood ratio test it is not required. That procedure is based on a simple argument that we consider maximization of the likelihood function under the full region and under the null hypothesis space and then we compare them. So, the logic is as follows. Consider the likelihood function L theta x that is equal to product of f x i theta, we maximize L over omega with respect to theta say maximization is L hat omega that is equal to supremum of L theta x for theta belonging to omega. Consider we consider maximization of L over omega naught with respect to theta and say maximization is L hat I call it L hat omega naught that is equal to supremum of L for theta belonging to omega naught. Now, you see if the hypothesis omega naught is true that means, theta belonging to omega naught is true then the maximization of the likelihood function over this will be almost the same as the maximization over the whole space. You can of course, notice from a simple mathematical argument that L hat omega naught is always less than or equal to L hat omega because this is maximization over a subset and this is maximization over the full space. So, we always have we always have L hat omega naught always less than or equal to L hat omega. So, naturally if L hat omega naught is closer to L hat omega that means, we have more confidence in the hypothesis omega naught that means, the likelihood that H naught is true is more likely. However, if L hat omega naught is much less than L hat omega then we have doubts over the correctness are beingover H naught being true. So, therefore, if we formulate the ratio L hat omega naught by L hat omega then for the smaller values of that we would tend to believe that H naught is not true. So, this is the basic idea for formulating the likelihood ratio test. So, consider the likelihood ratio. So, that is let us call it say some lambda that is equal to L hat omega naught in the likelihood ratio test we reject H naught if lambda is less than or equal to some k. Now, once again the question about the choice of k comes and therefore, we can choose k to fix the size. We may actually look at what is the probability of rejection. So, that is known as the significance testing we consider theprobability of this and we look at the range by which we will be actually accepting. For example, if I consider say alpha is equal to 0.01 or alpha is equal to 0.05 and we look at whether we will be actually rejecting. So, the maximum valuethe minimum value up to which we will be considering that will be called the p value of the test. Let us consider an example here say x 1, x 2, x n follow exponential distribution with parameter say mu this is where f x mu. Now, let us consider say we want likelihood ratio test for say mu less than or equal to 1 against say H 1 mu greater than 1. So, we consider here the likelihood function that is equal to e to the power n mu minus sigma x i and here it will be x i greater than mu for i is equal to 1 to n. So, naturally this is maximized here we can consider say mu is greater than 0. You may consider this as a typical situation where the lifetimes of components are following exponential distribution with parameter mu, but here mu denotes the minimum guarantee time the rate is 1 here. So, this is maximized with respect to mu when mu is equal to actually the minimum of x 1, x 2, x n. So, you get l head omega that is equal to e to the power n x 1 minus sigma x i the maximum value of the likelihood function over the parameter space. Now, let us consider to find maximum over omega naught, omega naught here is mu is less than or equal to 1, then it is maximized when mu is equal to minimum of x 1 and 1 because we are putting 2 restrictions mu is less than or equal to x 1 and mu is less than or equal to 1. So, the maximum value that mu can take is minimum of x 1 and 1.   So, that is equal to e to the power n minimum of x 1 1 minus sigma x i divided by e to the power n x 1 minus sigma x i. So, this term naturally cancels out. Now, this is equal to 1 if x 1 is less than or equal to 1 and it is equal to e to the power n minus n x 1 if x 1 is greater than 1. So, you can easily see that when the likelihood ratio is 1, you will always you cannot reject h naught because this is the best that can happen. So, we can say that l r t will always accept h naught if x 1 is less than or equal to 1. Now, let us look at the other region. So, when x 1 is greater than 1, we consider the rejection region e to the power n minus n x 1 less than k. So, if I take log etcetera and then adjust the terms, then it is equivalent to something like saying x 1 is greater than some c where c is to be chosen suitably. As an example, we may consider say probability of x 1 greater than c is equal to say alpha. Suppose, we want this for supremum mu less than or equal to 1. Suppose, we consider this situation. If we consider this situation, then this is equivalent to e to the power n minus n c is equal to alpha. That means, n minus n c is equal to log of alpha or we can say c is equal to 1 plus 1 by n 1 minus 1 by n log alpha. So, you are actually rejecting for a value slightly higher than 1. So, this is a typical application of the likelihood ratio test and also you can see I can show you through an example for the normal distribution that how does it compare with the standard test that we obtained using Neyman-Pearson theory. Let us consider another example. Say I consider x 1, x 2, x n following normal mu 1 situation and we consider the likelihood function that is equal to 1 by root 2 pi to the power n e to the power minus 1 to sigma x i minus mu square. Now, I consider the hypothesis testing problem say mu is less than or equal to 0 against say mu is greater than 0. Now, if I consider the maximization of L over omega here omega is actually minus infinity to infinity gives mu hat is equal to say x bar and therefore, you will get L hat omega that is equal to 1 by root 2 pi to the power n e to the power minus 1 by 2 sigma x i minus x bar square. But if we consider maximization over omega naught where omega naught is actually minus infinity to 0 then we will get mu hat is equal to see if x bar is less than 0 then it will be x bar, but it will be 0 if x bar is greater than 0. So, that will get give us minimum of x bar and 0 if that is happening then L hat omega naught that will become equal to 1 by root 2 pi to the power n e to the power minus 1 by 2 sigma x i minus x bar square if x bar is less than 0 and it is equal to 1 by root 2 pi to the power n e to the power minus 1 by 2 sigma x i square if x bar is greater than 0. So, we can put less than or equal to 0 here it does not matter now the thing is. So, the ratio that is L hat omega naught by L hat omega if you see that is equal to 1 if x bar is less than or equal to 0 and it is equal to this ratio e to the power half sigma x i minus x bar square minus sigma x i square if x bar is greater than 0 that means always accept h naught if x bar is less than or equal to 0. Now in the other case you will formulate the reason here when x bar is greater than 0 we reject h naught when e to the power half sigma x i minus x bar square minus sigma x i square is less than k. So, if I take log here and adjust this half here it is becoming sigma x i square minus x bar square minus sigma x i square is less than some c. Now this can be further simplified here we can consider this as sigma x i square minus n x bar square minus sigma x i square less than c. So, this cancels out. So, we get actually x bar square greater than some c. So, rejection reason is turning out to be two sided something like modulus x bar is greater than some c 1 that is called it c 1 this as c 2 here which is a. So, actually we can again see here here I am considering x bar greater than 0 this is equivalent to x bar greater than c 2. Since x bar is positive this reduces to x bar greater than some c 3 kind of thing. Now if you compare it with the Neyman Pearson test there it would have been root n x bar greater than z alpha. Now here it is like this only in this particular portion, but when x bar is less than 0 we are always accepting h naught. So, there that is the difference from the Neyman Pearson test. So, notice the difference from n p test for x bar less than 0 case, but if x bar is greater than then it is, but for all practical purposes you can see because alpha will be sufficiently small. Therefore, z alpha value will be very close to high and therefore, the two tests will be practically the same. In the parametric methods I have concentrated mostly on the point estimation confidence interval and testing of hypothesis problems in the. So, there are other cases also when we do not have the parameter is specified that means the distribution is not specified and we consider distribution free methods. However, that will be slated for a different zone. Now we will be moving over to another topic in this statistical methods. So, that I will be starting from the next lecture.


Hi, I'm going to talk about one way I teach compound words to my students. So a compound word is two words put together to make a new word. So for example, star and fish put together is starfish. So what I do is I use a hand movement to help my kids remember it. And so I'll say say star and they'll say star and then I say say fish and they'll say fish. And then I'll say I'm going to put it together to make a starfish. And then we do it together a couple more times. So we'd say starfish, starfish. And then we'll do several words together. We'll do some more together. We'll do fire, truck, fire truck. Or we can do rain, bow, put it together. What is it? A rainbow. And that's one way I teach compound words to my students. Thanks.


So I'm filming right now on a GH5 with this new lens right here. This is and I'm in intelligent auto mode So everything is auto. Let's see how it's going with the autofocus and everything. This is the new lens a to 18 So hello, so who are you? Hey, I'm coming last minute again. Okay. I've met you before right? Yeah, we're gonna start talking so we got a little friend of a cowl here, but no talk about cows We need to check this new lens. There's a people excited about a to 18 Because it's super wide so primarily with our lenses again The fact is we listen to our customers and we wanted to get something really wide and to kind of show people what our cameras are Really capable of this is a super wide angle lens. It's 8 to 18 mil. It's the Leica It's really sharp. So awesome for a kind of night street photography as per photography. It's weather sealed So really nice piece of kit. Is this for video blogging or not like the stuff that I do probably not really but to be fair You know with the fact that it is such a good piece of glass and it's so smooth You could easily use it for video. There isn't a problem using it now. How do you feel? It looks very in focus right now? I mean what I can see right here because and There's no dual is in this because you don't need it for so such a wide lens Well particularly the fact is that you know, this isn't it's the same as it's not a constant 2.8 It's about size and weight We didn't want to make a really big heavy lens that people are just not going to use again So it's about having it compact to get in the very best optics, but but bear in mind that we've got the body Stabilization so you're only at 8 to 18 so you don't need a long reach or you're not going to have a long reach So therefore you don't really need the stabilization. You've got it in camera. So you don't need it in the lens So I'm fully zoomed in right now. I'm moving around the cab moving around you just handheld This sensor stabilization of the GH5 is mind-blowing. Oh, it's so good, right?  I'll tell you what let's hop into the center Yeah, so we actually did the lens show here in London. It's the Wex lens show and they do it every year We came down last year and we're here again this year. It's been a massive success You know, we love interacting with the people we love bringing brand new kit This is an exclusive on the 8 to 18 and you know, we've brought it down so people can see it here first It's important that people kind of keep abreast of what's happening within the industry, but we give exclusives We're not just going to go to the big shows and you know the Wex lens show here in London is a big deal for Wex It's a big deal for the industry That's why we bring this kit and we show them First here. What is this place here? Looks crazy. It's all right. It's um, this is the design sensor So, you know, it's all about design where London was designed not where London was designed that'd be mad Let me show you the show come this way So the lens show it's a cool show about cameras. It's about all right cameras. It's about kit It's about the latest products. They're kind of getting all the manufacturers here with us. Um, we've got everyone that come down from Sony Nikon and everyone else but we're the people that are bringing brand new kit to the show We're the people that are actually showing world exclusives here And that's with the 8 to 18 you have you've had a pretty busy couple months, right? I've been crazy busy, you know What are people doing here? They're actually buying the This is Wex photographic Wex photographic actually bring down kits So they've got hundreds of thousands of pounds of a stock that they've brought So you can actually come down and buy the kit here So you can come down see it as an exclusive And then you can come to the tills and actually purchase So you don't have to go away and think about it. You can actually buy it here at the show Okay, so we can actually see there's a bunch of gh5 there or no more stock, right? We sold out we sold out, but you know, we're not going to grumble at that But there is anamorphic lenses. We've got lots of people upstairs downstairs We've got a stand out at the back. You know, we're not afraid to kind of bring our kit down and show people Absolutely what it's capable of and let people get hands on with it. Come have a look at the stand. It's just down this way right So, um, how you doing with that stabilization? You doing okay? Yeah. Yeah. I mean the I was a little bit disappointed that they didn't have dual is this lens But for sure it wouldn't even work right because it's very very wide. It's very wide and the fact that, you know, again It's only there for under 36 mil. You don't need your life. You only need stabilization on one form It's pointless overworking something just for the sake of it All right, let's go uh to your booth. Let's check it out. So here we are just at our stand As you can see we've got a whole breakfast. It feels a little bit like deja vu this video. I know, right? Who are we going to start talking about as we keep meeting up like this? But every time you know that we've got something new So the last time we had the gh5 brand new and now I've got a lens to go on that's brand new as well And this one this video. I'm happy. It's not flickering right now. So what do you do to my settings? So you want to film in 60p the phone with 60p is when you get any lights or anything else It goes out of sync. So what I've done is I've changed that to 50p for you So you shouldn't be getting any flickering at all That's right. Yeah. Yeah, I'm using the new just bought today the Saramonic uw mic 9 so we have a dual lav wireless So that's the sound hopefully the sound is okay. I think for video blogging. It's actually quite cool to have a very wide It the point is you know, particularly if you're shooting in 4k and you only want hd content if you shoot really wide You can then crop down to hd. So when you've got four times the resolution of hd You can crop down see you're doing second cameras things like this. So if you shoot really wide You can crop down so it looks like you had more than one camera at the event And I would say I'm a little bit big as a person. It makes people slimmer, right? Well, I'm hoping so When I watch this video back, I'll be holding you responsible if I don't know really slim. No, no, you is perfect I'm just saying, uh, okay. Let's check here the booth. Uh, I was I was trying out the Uh, can we grab this one? So, yeah, let's grab this one. What do you think about this lens here 42.5? 42.5 is one of my favorite lenses for portrait. It's an absolutely beautiful lens So you want portrait work or anything like that and you want to use ambient lighting Absolutely brilliant.   How can it be so much bokeh in this lens? What is the science in there? 1.2 and it's about the glass, you know, you can see from this lens here the amount of glass It's involved again. It's one of our premium Leica lenses if we have this standard 42.5 You'll notice it's a much smaller lens in its body So we're looking at Leica, Leica, three big Leica lenses It's like a story, right? It's 12 to 60, which is also the big seller, right? Let's go over the Leica 1260. Is that the most demanded one for the GH5? The GH5 12 to 60 Leica kit is our most demanded kit. It's quite funny really because we knew that videographers were going to be after this So we kind of expected to be with the bike body only and use historical glass And actually because of the quality of the 12 to 60 Cells of outstrip demand hugely So, you know, we're actually struggling to keep up, but we'll keep fighting through because it's a nice battle to have Nice So this has been an official announcement that there's going to be a bunch of firmware updates, right? There's going to be a autofocus improvement Well, to be fair, we constantly improve every aspect of our cameras using firmware updates We've already done one, so anyone that's got a GH5 should already have 1.1 installed on their GH5s If not, go on to the website download it and update your GH5 to 1.1 1.1 added something with full hd, no? That's right. Yeah only with full hd The point is, you know, there are often little tiny tweaks within an update That we kind of don't shout about because they're only minor improvements But it's important that everyone just updates each time we do a firmware update Uh, all right, and it's easy to update just go on the website download it onto a small sd card Put it into your camera press play and away it goes the updates itself So how much demand is there for this new lens the 8 to 18 is going to be a blockbuster a good Well, we're hoping so we're hoping so You know, we're chasing the whole dream of having very high quality glass And that's what it's all about because you have they're here the somewhere that You have the the 7 to 14, right? What's the difference between the 7 to 14 lumix and the 8 to It's the quality of the glass. So, you know, primarily this is a very very good quality glass And we all know that if you to get one glass one lens that has average quality glass and another one that has exceptional quality glass The image at the end is hugely improved. So if you look at the 42.5, we do two of them Um, and the not to chron is an amazing lens So primarily that's the reason why it's the portrait photographer's choice How is uh This lens, how is it in the corners as people are talking about the corners have to be sharp or what? How does it work? Well, that's why we use Leica So Leica basically will tell us if we've getting any kind of aberrations or any kind of issues at the edge of the glass And they'll work it through and will we basically feed back to them? And when it's perfect, then we release it and that's what we've done. And so it's perfect. It has a As a hood hood. So does it lock in like the the nice new way? Absolutely So you've got you know, but on there that's your release and then you just completely remove it And as you can see on the front there, it's got it's fully threaded. So if you want to fit any kind of filters Yeah I just clicked by mistake the display button. So it turned off my viewfinder. Okay. So I'm still there Yeah, so you've got a fully thread on there. Are we going to fit any filters or anything else that you need? So you can put filters. Yeah, ND. Is that what people want? Yep ND filters. What else is there? And well primarily that's what they'll use it are ND filters more than anything else purely or heavy filters if you want to dial down to stop or so if you want to do long exposures during the day You can fit filters for that.  Oh, they buy GH5 with the 8 to 18. There's no kits yet No, no and primarily that probably won't happen But there's always going to be, you know Things in the pipeline and if a demand is there and we get asked enough then obviously it is something that we can think about But currently the 12 to 60 is a really good range. You know, it's equivalent of 120 mil So it's a good focal length and you can get it in two different qualities So whether you want it as a standard kit lens or you want the life of quality You can go either way as a as a kit. So now I'm tracking focus Half press half shutter press. I'm not sure if I need to do that But basically I'm just clicking once in a while on your face if I get out And it seems to track very good. I'm zooming in right now. I'm going to zoom out again And uh, so it should people should be happy about this lens, I guess Yeah, I mean the lens is good and you know as far as being able to hand hold the camera and run around like we have Realistically it's you know a thing that people should embrace. Let's let's go back over here There is a There's a 12 to 35. Is that the mark two? Yes. So That's a constant 2.8. It is. I mean it's brighter than the Leica Um, well, it's constant 2.8. So primarily out there far in but as you can see from the size of the glass You know, you are gaining a lot of glass on here compared to the 12 to 60. I mean Compared to the 12 to 16 slightly slightly. Yeah, so that means when you fully wide it's brighter than the other way Yeah, yep, but you're then going to have the trade-off of you know, the Leica glass is incredibly good glass So 12 to 35 we also do the 35 to 100 and these are the mark two versions. So these are the reworked Um, which work better when you're videoing. So when you're stepping down Um, and they also work better with the dual is because they've been built for that purpose Can we quickly check the g-series? Uh, there's a story about uh, you have uh, Is this the new super compact one? Yeah, so this is the gx 800 The gx 100 is very similar to the gx 80 apart from what we've done as you can see on the back is to remove the viewfinder So remove the viewfinder because not everybody wants one and the fact is that if you don't want one You don't need to carry one. So it's much smaller On there. We've also got our compact 12 to 32. So it's a collapsible um 12 to 32 lens So what it actually does is it extends out Nice And we've also put a hinge So you are not fully articulated, but it's definitely very handy It's very affordable if you want to do you want to do selfies I wish it had a little microphone input Okay, okay. Otherwise, it's fantastic.   Yeah, I have lots of wishes And do what I'm talking about. No need for that. Okay, that's great. This is very affordable, right? Yeah, it's really cheap. Uh, you know, you're looking around the 500 pounds mark Um, so it's basically if you want the quality of a micro four thirds camera Um, and you want the Benefit of a large sensor in a very compact camera. This is the size of a compact camera Let's put the 8 to 18 on that one The 8 to 18 that's not particularly exciting What we could do is you could right we could any any micro four thirds. So why aren't we stupid?   Well Cool. So, uh, there's lots of uh, lots of cameras Lots of cameras, lots of fun, you know people should come down and see us. It's a very cool thing