Good morning. How are you all this fine Monday morning? I don't know about how you guys are seeing this, but on my iPad were sideways despite the fact that it's oriented correctly on my phone, which is what we're broadcasting with. It seems like I'm always having issues. Nope, it goes sideways. It doesn't like the iPad. I don't know. They need to fix the app on the iPad. Alrighty. I hope you guys are all having a good day. Good morning, Ruth. I had to make a third cup of coffee because, you know, some days are just like that, right? You need an extra cup of coffee. Good morning. Hi. How are you? Okay. And I'm going to clip this wire out of my way because like I said, I'm having one of those mornings in this hanging wire, which you can't see unless I do this. Yeah, that's going to drive me crazy. Life is good. You know what? I'm on the right side of the dirt, so it's all good. Cold brew.  It's all their fault. I love coffee, cold, hot, sweetened, unsweetened. It doesn't matter. If you let me, I would drink it all day. That's really bad for you, but yeah, I do try to limit how many cups I have. All right, so we're going to do some Monday with decor this morning and I pulled this actually off of my studio wall. I actually did 10 of these little paintings last year. I know, right? And I gave all of them except this one away as gifts. They were gifts. And this is one way to do faces. These are faceless girls. And they're easy way to do a face, an interesting face, and to do it without a lot of pressure. And to learn about shading and get something that is suggestively realistic and interesting without getting too fussy. So we're going to work on this this morning. So you brew it cold and you drink it hot. You know, I love coffee. Any old way. I guess I shouldn't do that. My whole table shakes a little bit. It's like we're on an earthquake. We're not really. All right, so I've got some more little four by four canvases. And before we get started, and we're going to like do flesh tones today, mix flesh tones and acrylic. We did it in watercolor on Wednesday. But while we're doing that, this first layer on here can dry. Now when I did these, these are all paint and then some Stabilo pencil or that might be charcoal. I don't remember now. Hello, Lisa. I didn't do any collage first that I remember, but on these, I thought since I have these really great papers. My screen is sideways on my iPad on the camera on the phone. It's fine. I will reorient the picture when I load it to YouTube. I don't know. Deco art has these deco paid Americana deco page papers. They have lots of different patterns. I pulled this one out of the things that they sent me. This is the Victorian romance set. I was attracted to these colors. Auto correct is not our friend, Jerry. It auto correct. So I ripped off a few pieces and I thought we would put these on here first and let them dry while we mix some flesh tones. Also, while we're doing this, you guys don't be afraid to ask me questions. Yes, we're doing kind of a free mini art lesson here when we're live on Periscope. But also I want you guys to start using this as an opportunity to ask me questions as a Q&A session. I will always do a little bit of a demo for you while we're on here. But I do want you to feel free to ask me questions about art or artistically that you're having a problem with or anything like that. So I'm just using this is fluid matte medium. I normally would use deco page, which is by deco art because I really like their deco posh medium, but the matte medium dries a little faster. And in this case, because we're live and you guys don't want to wait eternity for things to dry, I figured it might be more advantageous to use the fluid matte medium. But definitely if you're not nuts like me and live on camera, I would use the deco arts deco page because I think it works really well. I'm not worrying too much about, you know, how these are going on or which way they're oriented. This is just to give which way they're oriented or anything. I do have to learn to finish my sentences. Don't I? All right, I'm just getting some pattern and texture on the canvas. I will try to do my standard warning here.  And I get tired of you all asking to see my boobs because honestly, I'm 52. They're not that cute anymore. I had a fence. Some of you are people. I'm sorry. I just realized that might be offensive. Oh, well, see, I got lots of lots of hearts there. All right, so I like that. I also, for some reason, I like this like old fashioned flower print. I don't know what's up with that this morning, but we're going to put that I know, right? It's talking to my husband about that.  I don't know. Nobody wants to see that. They keep asking, but yeah, they were. You know, that was a long time ago. All right, so I really like there's something about this paper collection this morning that's just really caught my eye. So I'm going to put some of this on here. I want to put and I was thinking I would just use one or the other of the prints, but I'm really getting the urge as we're sitting here to put all of these on here. I know, right? These people are funny. I try to look on it like Shannon Green does and she kind of makes fun of all the trolls on her YouTube channel. So and I think she's on live right now. Dang it all. So I might be losing some viewers to Shannon being on. I know I'm not sure if she's here on Periscope if she's on YouTube. I did get a notification right as I was going live, but I wasn't paying any attention because I was trying to get ready for you all. Yeah. I don't think on purpose she does. Yeah, exactly. Some, you know, some people have sad, lonely lives and I'd feel sorry for them if they weren't so aggravating. Right. So we're going to put that matte medium out of the way because that's the last little bit I'm going to need to put a piece on here.  You can do little mixed media pieces on them, faces. You can do lots of stuff with them. You know, almost everybody.  Let me just instead of trying to wrap that around, I can do happy. You can do happy trees. Definitely. You can do happy trees. I did a happy tree. So I'll show you. I did the periscope hop thing where we were celebrating Bob Ross. Okay. So now we've got these and they're all covered with our decoupage papers and the matte medium. And it's going to just sit here and dry. I'm going to put them to the side in the last couple of live Mondays with decor. We did our sunflower. And this is the one I did on the periscope of hop with the happy trees. And today we'll do some faces. First, we've got to mix some flesh tones. Any questions you have about me, where to email me, how to get a hold of me, where my online shops are, my Facebook group, my newsletter email list, all that stuff. Go to GinaBairns.com, it's all there. All right. So the other only thing I have that's not deco art this morning is my Stabilo pencil because I do think we're going to want to use that. But we're going to need a palette knife. This is one made by Decowart. I love the green color, don't you? And I've had a lot of plastic palette knives. Oh, yes, please. I love the hearts. Oh, and I love brown. I love the plastic palette knives. And this one, I've broken a lot of these in my day, but I love these green ones. They seem to hold up pretty well. Need a rag. All right. So we're going to start by mixing some orange. I have the Decowart Artist Traditions Sampler set here. You can get these. I think they have 12 little bottles in them, including some paints and a couple of mediums. And we want a red and a yellow. Now I'm going to show you a couple things. So there's a couple of reds here, but one of the reds is a lot more purple than the other one. This is red violet and this is Nape's all red. So it's really best when you're starting to practice mixing skin tones. Use the sample that you're shooting for as your own skin tone. That just makes it really easy. And since I'm pale and pasty, we'll use that color. Pale pasty, is that a color? Then I'm going to add a little bit of Hansa Yellow to both of them. And we're shooting for an orangey color. And when I mix flesh tones, normally I mix a lot of it. And then I will put it in a small separate container and just have it around. Now, because this violet one already has some blue in it because it's violet, you're going to already get this interesting color. Yeah, this is actually, no, this isn't a palette plate. This is a white ceramic plate from the dollar store.    Good morning, Cindy. So this was already kind of a nice, purpley flesh tone already, a dark color because it already had blue in it. This one is not, it's very, I don't know, anybody who's really that color. So we need to brown it up a little bit by putting some blue and I'm going to use ultramarine blue. Now, any of you that know me, especially my friends on here, hey, any of my friends on here who know me, Cindy, Jerry, I hate mixing colors and if I can help it, I just buy the color because I know how, but it's not my favorite thing. So you're shooting for a dark flesh tone color. Now, I have not ever done this and had it come out exactly right the first time, like ever. That's still too red because I don't know anybody who's really even a dark flesh tone is that color. So I'm going to add some more blue to that. Now, if you're worried about, yeah, if you're worried about getting, having the paint dry out before you're done, you can add some extender, that go where it makes an extender, which extends the drying time of the paint. And I'm going to add a bit to both. That's better. I'm liking that better. So now we're going to add some white to both of them. I did pull out a couple bottles of the big bottles that I have because there's a couple colors that I like that don't come in the kit that I might want to use. So now I'm going to take, and I'm going to add some white to half of that dark color I made. And if you only do half, then you have a darker shade of the same flesh tone that you can use for the shadows. This is a deco art. All of these items that are using this morning, you can get at decoart.com. They should also have them at your local arts and craft store, but I would, if you're like me and you have multiple issues with going outside, not only anxiety issues, but right now this time of year I can't go outside because of all of the holiday candles and pine cones, and I'm allergic to all of them. So I do lots of online ordering, and that's just easy. So looking at these two flesh tones, I actually like this one better than this one. I think this one's still a little, this is a little red. I might need to add some yellow to this one. So when I'm mixing flesh tones, if I get a color that I like, then I just mix a whole bunch of it up, and I save it in my little containers, and that way I don't have to worry about doing it again. That might be too much yellow, but we're going to find out here in a minute. So like we did in one of the first deco art Mondays where we mixed every color with every color to see what we would get, and we made kind of a color chart. This is why you should do this. Okay, see this is what happens. Then you add a color to fix it because it's too red, and then you make it too yellow, and that's not bad. Putting it next to my skin tone, it's not horrible. I mean, you know, I'm going to end up not using a lot of it, so it's okay, we're going to leave it, but you could keep mixing it and mixing it until you get something that's exactly right. When you do get something that's exactly right, what I do recommend that you do is make some notes.  All right. My desk is a mess again. Why is it every Monday morning when we do this? My desk is a mess. All right, we're going to move this to the side here. Put my brushes in the water. I've got my rag. These are just about dry. So, let's do a faceless girl first, and then we'll do one with features. Wait, I need a coffee. So, decoart.com. DecoArt makes the American brand. DecoArt Media. DecoPage. They make a lot of different products, Andy Skinner stencils and products, and I really like their paints. I'm pretty impressed with them. All right, let's see. I'm going to start with a Filbert, my preferred paint brush, and this is number two. See, I know that I have a couple of Amish dolls, and I like that. Let's see. I don't have my glasses on. Number eight Filbert, sorry. All right, so we're going to start with the flesh tone, and I'm going to pick this one. I'm going to just follow my instincts. I'm going to put in an oval for the face and at least part of an oval. And the neck. Because you don't do a floating head, that's kind of art no no. A neck and a shoulder. Now, you could do two heads, like on this one I did two, like two friends. You definitely could do that. I'm going to put out on my palette some white, some aquamarine, Americana, Neon, and Tord Orange. Americana, Neon, and Sizzling Pink. These are all colors that I use when I do these paintings a lot. This is the same Americana, Neon, and Scorching Yellow. And then I'm going to use Phthalo Blue, and I've got some Raw Umber, which is a dark brown. And I think I want some Quedocratone Violet, which is this other big bottle that I pulled out. That's a nice color palette to do this with. So now going back to my Filbert brush, I am going to grab some of the Neon Orange. I'm going to decide where my light is coming from. And I think it's going to be coming from the right. So I'm going to start just dabbing in some of the orange. I'm not going to really clean my brush. I'm going to, at least for the moment, I'm going to keep it kind of dirty. It'll blend with the orange paint that's on here. I'm okay with that. Remember, we're doing a faceless girl. I'm going to clean it off a little bit now, and I'm going to go into the Aquamarine, and I'm going to use that on the other side of the face where the shadows would be, where it's not in the sun. Don't be afraid to like get your fingers in there. This is about suggesting a face and not, this is not a realistic face. Not by any stretch.  I'm going to take some white. I'm going to put the white in where the lighter parts of the face normally would be if I was going to paint features in. I'm going to sort of smudge it with my fingers and move the paint around. Remember, we're not painting features. We're suggesting features, but we're not painting features. Okay, while that dries a teeny bit, let's put some hair in. I'm going to take some of the dark blue that I have here. Suggesting some hair. No, don't do a suggestive face, but then paint lots of details in the hair because then you just kind of shot yourself in the foot. We want the whole thing to be real suggestive. I'm going to grab some of my brown and some white. Now, if you get a mark on there that you like, leave it, go with it. Work it in.  And then I want to do something down here. I don't know what that means. Is that Russian? I have trouble with English. It's really terrible. My grandmother was born in Italy. Don't speak a word. My husband is first generation. His family was from Germany. Don't speak a word of that. I can say spoken to English, and they say nine and then I'm in really big trouble because yeah, that's as far as I can get yet. I'm going to suggest the cheeks. And you can use this neon pink. No, I'm sorry. My daughter's boyfriend is Lithuanian and she's learning to speak that, but you know, again, me, I have trouble.  And this is not about covering up your brush strokes or anything like that. That's where we are right now. That's cute. I'm going to use the dark shade of my flesh tone now, and I'm going to come in here. Now you could use, leave the blue in there. The blue is a great indicator of shadows, but if you want to do something that's, you know, a similar idea, but with some more realistic flesh tones than the goofy ones, then use your dark flesh tone as your shadow color. Then the other thing I want to do is I want to kind of mute the background a little bit. It's a little bit too bright and competing with the face.  So I'm going to take some of our white and I'm going to take, let's see, some of the aquamarine and a little bit of the yellow makes something that's a little more greenish. I'm going to put it in around our figure to just kind of mute the background a bit.  And don't forget to put some paint on the sides of your canvas. Okay, you all must just love watercolor Wednesday way better than Monday with Decor, because there's only eight viewers. I'm glad to have eight of you. The die hard ones. I'm going to put some white in here a little bit too, just with my finger. Hey, Mark, good morning. Okay, now before you call this done, thank you so much. I'm glad to hear that. Okay, so before you call this done, you want to further define your girl by giving her a few lines. Now, if the paint was dry, which it's not, and I would not recommend doing this until it was dry, because we're doing this live. We don't have time for that. But if it was dry, I do really like these deco art glass paint markers. Now, I know they're intended for glass, but the black and the white are very opaque and they work really well on lots of different surfaces, including canvas and fabric. So I really love them. But you will ruin the tip of your marker if you use it on wet paint, and that's true with any paint marker. So we're going to come in here with a Stabilo pencil, which is a water soluble pencil, so it doesn't care if the paint is wet. We're going to come in here and we're going to give her some lines and we're going to define the shape of her top, the shape of her neck, the shape of her face. We'll give her hair some lines to define that too. And there you have it. Now, you could collage a little inspirational word or quote on there and that would be a really cute Christmas gift. Just a faceless girl. So let's put her up here and let her dry. She really is cute. I'm going to have trouble giving her away. All right, now let's do another one. You guys let me know if you have any questions. Wait, I need a sip of coffee. I don't know how to share the video while I'm broadcasting, maybe because some of you guys can do that. We are painting mini canvases, four by four canvases with decor art products, creating some little Christmas gifts. I just did this one. We're going to do another one. Alrighty, so let's go with a smaller brush. You know, I spent a lot of, that's such a loaded question for me. I spent a lot of years in retail decorating a lot of Christmas trees. Christmas is not my favorite holiday. I don't like decorating Christmas trees anymore. That being said, I love spending time with the family and we will probably be spending time with my daughter's boyfriend's family and also my mother-in-law, who's not getting any younger and we like to spend as much time as we can with her. So I'm going to start with a light flush tone. I'm mixing some white in it. I'm making a really light color. And you notice I'm using this one that we made with the violet red and I'm really liking this color a lot. It's a really great color. My husband is German, so a lot of our traditions are based in German traditions, but we usually celebrate on Christmas Eve. Spending time with the family, going to church, it's really not a fan of doing a lot of the other crazy stuff, all the shopping and all that stuff. Okay, so now I've just outlined my face like I did the other one. And you know what? Since we're doing a more detailed face, let me see if I can zoom in a little bit. There we go. Fixed my chair. All right. So we've outlined our face with the light color. Now I'm going to come in and I'm using the same brush and I'm going to just start painting in the highlight of the forehead, the bridge of the nose. There'd be a light spot under the chin, the cheeks, painting around things. Then I'm going to take the dark color, the shadows in. Put the dark color in the shadows, I should say. Now your face is going to look a little odd until we get all of those details in and until we get the whites of the eye in. So I'm just kind of blocking in the lips, the nose, the area around the eye. Maybe the suggestion of the eyebrows. I want something with a stiffer. Here we go.  I've had it so long I don't even know what it is, but it's a teeny tiny little flat. It's really great for these small canvases. It's good for blending. So I'm going to just blend some of this dark paint I put on here into the light paint. I'm not going to blend it completely. So then what happens is you get the dark shades, but then you also get kind of the light shades, but then you get also medium shade. And because we put the extender in the paint, we don't have to worry about it drying too quickly. Oh yeah, this brush is going to work much better. And this is just the first layer. Yeah, you need a detailed brush and I like a small, short, flat brush with like stiff bristles for doing this kind of blendy thing on this small canvas. Normally I would just use my fingers or something, but this canvas is too small for that and my fingers are too big. All right, so now we're going to go in with, I'm going to go in with some white and we're going to block in the eyes. Can you see her coming along? Maybe. So I'm using the light color again. I'm going to wipe my brush off on my rag to get the excess paint off and then I'm going to blend in some of this paint, the light color I just put on here. And it's really just about layers and blending and don't worry about, you know, losing any part of the painting and treating anything too preciously. You can always bring it back. One of the joys of acrylic paint is that it really is all about layers of mark making. I'm going to use my neon orange to represent, of course, I'm sorry, to suggest sunlight and brightness and warmth. So I'm going to put in a little bit of the neon here. I'm moving around the canvas and that's giving the eyes a little time to dry. I'm going to take some of the neon pink, dab it into the cheeks here a little bit and wipe my brush off and using a dabbing motion, just blend those like little blobs of paint in a bit. There we go. She's looking pretty good. Let's do something with her hair while we let her face dry a bit. Now, you notice I suggested her lips, the upper lips darker than the bottom lip. That would be normal. The bridge here for nose and the ball of her nose would be brighter. There would be a shadow underneath the nose and two shadows for the nostrils. I did suggest all those while I was doing the painting. Also, there would be some shadows around the eye. Now let's do the hair. I really like giving my girls blue hair. I do not know what's up with that, but let's do it again. We're going to use the dark blue that's on our palette.   I've got to go buy some stolen. Either that or make some. I don't usually make it. I know how, but it's easier to buy it. It's my favorite Christmas cake. I know some of you are like, ooh, because it's like fruit cake, but I like stolen. I don't like American fruit cake, but I like stolen. Now I'm putting some brown. Similar colors to what I did on the other one. Hey LP Red Flower, how are you? I was trying to catch up on everybody's YouTube videos this morning that you all posted on YouTube this weekend. She's got a cute hairstyle, but it's really dark, right? We did with the other one. It's white. Now, although she's way more realistic than the other one in that we're going to paint and suggest some features. I don't do anything that's super realistic. So she'll still be pretty suggestive. And we will still be coming in with a pencil and doing some stuff there. Hey, thanks guys. I made her hair a little bit too light.  So you want to make sure in any painting that's true whether you're working with watercolor or acrylic or any oils, whatever medium you're working in, crayons. You want to make sure your paintings have a good balance of light tones and dark tones to make it look interesting for the most part in my opinion. So this is some of the brown and I'm just adding layers of marks to her hair to make it look interesting.  Baby wipe. See if I can do this without making a big mess. So baby wipes are great for painting with acrylic. They will get a lot of stuff off. I might have to just work that in because that's not wanting to come off. I can do that. So sometimes what did Bob Ross call them happy accidents? This is the shadow side of the face anyway. So if I was going to get some blue on one side of the face, this was a good side to do it on. So I'm going to work it in as if it was part of the shadow color which I probably would have done eventually anyways. Let me know as we're going if you guys have any questions. I'm going to bring some of the blue down here just to make it look cohesive. That looks pretty good. Let's do a little bit here too. I knew I wanted to do faces this morning before somebody asked but no I didn't plan it beyond that. I know somebody is going to ask at some point. I didn't plan it. I know I almost never do. I just start painting. Oh thanks, Cheryl. These little canvases are fun to do. They're easy to practice on and they're great to give as gifts because everybody has room in their space for a small canvas. If you're like me and you've been on this planet a few years and you've lived in your house for a while you don't have room on the walls but you have room for us not for something big. See? But you have room for little ones. I always thought it would be cool and someday in my dream studio I'm going to do this so you guys should be prepared. I want to do like one whole wall that's covered in little mini 4x4 canvases from all of you guys.  Wouldn't that be cool? Okay. While her hair is drying a bit I'm going to go back to her face. See I sometimes wish my walls were more bare than they are but I've lived here a long time and I'm an artist and they're just not they're just not bare. I know I have to work on it right Cheryl maybe it's something I need to add to my list for next year because I think it would be so cool. I have a little wall by my doorway that's got a few pieces on it from different friends and fans of you guys things you've sent me in Happy Mail but I don't have like I just think a bunch of little canvases all in the same size would be fun.  I'm going to work on the background and I'm going to even do the background before we do anything with giving her like clothing which you don't have to do but I like the idea of doing that. I'm going to I'm going to put some yellow back here this is the neon yellow a museum of friends art. Yeah that's exactly what it would be. So yeah when you're working on faces one thing I struggled with in the beginning is you know really just getting anally compulsive and wound up about the shading being perfect and the thing I like about being an expressive painter is that it doesn't have to be perfect. In fact it's about it not being perfect and suggesting things with different marks and I love that and that's perfect for me. Otherwise it was just adding to my anxiety disorder level and that was just not a good thing. Not that any stretch of the imagination was that a good thing. So now I'm going to add some of the Aquamarine turquoisey green colors that we've got on our palette. I'm just laying them in over the background pretty randomly making sure to get some color on the edges and the only way to get better at it and to get oh thank you to thanks Jerry and to get something that you like and to start develop your own style is to just practice. There's just there's no shortcut unfortunately because you all know I love a good shortcut if there was one I would tell you but there's not. I also took a lot of classes with a lot of different artists and watched a lot of YouTube videos and tried a lot of different things and that's the other thing to do. Alright we're going to let that dry a little bit. I like that. As I say that I'm thinking oh wait wait wait so I'm just going to with my finger you know I can't do a canvas without getting my fingers involved that just never happens. Okay yeah now I can leave that to dry a bit. Let's do something with her eyes. I have a small detail brush here. Let's see did I grab a little one. I think this will work it's got a good one with a good point on it. This is again it's all worn off but I'm pretty sure this is a Donna Dewberry one stroke painting brush and it's just a really small little round brush with a decent tip and I am going to for this now before we get started I'm going to get some carbon black out because we will want it oh that's just plenty a little touch of that. You didn't see that off camera it just splattered on my plate so that works. I am going to start with mixing my blue and my brown that I have on my plate. I have raw umber and phthalo blue it's going to give me a dark brownish blue and I'm going to use this color and we're going to here on my brush sorry we're going to use this to suggest an eyebrow and I'm barely barely touching the brush to the canvas. Oh yeah I'm on here live every Wednesday and every other Monday and it's a great time to ask me questions and stuff so I look forward to seeing you back on here again. So that's just a suggestion of an eyebrow I made this one a little too long so let's just get a damp brush in here while the paint is wet and fix it. There we go. Now I'm going to use the same color that we mixed our brown and our blue together and I'm going to come in here to the top of the eye where the eyelashes would be and I'm not going to really paint all the eyelashes in but I'm going to just put a dark line there and that's going to suggest the eyelashes. Again I'm barely touching the canvas if you get a smudge use it to be your advantage and let it help you suggest another feature on the face or shadow. I'm going to just put a little bit of this dark color where the nostrils would be I'm going to put some of this color here in the lips between the two lips the upper and the lower lip and then I'm going to get my little flat brush out and tap it off on my rag so it's not too wet and I'm going to just blend that into the upper lip oh yeah that's perfect and then I'm going to put some underneath the lower lip there would be a shadow right there and then I need to decide what color her eyes should be let's do blue actually I'm going to mix a little white into the same dark color we've been using and I'm going to we're going to try something why not I'm going to put a little bit of that on there now it's like a greenish blue color which that's a good color then we're going to take some of our aquamarine if you look in the mirror at your own eyes there are not the iris which is the colored part of the eye is not all one color there's lots of colors in there okay that brush was really wet and I just got too much water on there so let's see if we can lift it a bit like I have brown eyes but if I look in the mirror there's lots of amber colors and some really dark black colors in my eye now I'm going to take some white I'm going to touch up the white part of the eye which is called the sclera I got too much on this one oops see one of the good things about doing these live shows is you guys see I make mistakes just like you all but what did I say about acrylic paint is about layers of marks so if you don't get it right the first time don't freak out just let it go let it dry and just keep going and make marks so now this is black so I'm going to put the black in the middle where the pupil would be I'm going to run a little bit of it on the upper lid well see you didn't see the mistakes so no big deal I do make them I make plenty of them so now to make her eyes have a little bit of life you want to add a little bit of white like a reflection now I like to put my fingertip over those white dots after I make them and that just smudges them and makes them a little less perfect I'm going to go back to our neon orange this will be on YouTube you know it takes me a little while to get them onto YouTube I try to format them with my fancy video software so that you get as big a picture as I can and I have to reorient it and then save it and it's kind of a huge deal but so it takes like a day to get all that done but it will be on YouTube I know what I did there but I did something that I don't like because now she's got a dark spot on her cheek now for the new year for 2016 we will be still doing the live periscopes at least once a week we will be still doing tutorials but I will be doing more detailed tutorials on you to me and I have paid paid classes on you to me that does not mean I don't want you guys to freak out which is why I'm telling you now it doesn't mean the free stuff stopping because of course it's not I wouldn't do that to you but I've got to make some money somewhere so we're going to be doing some in depth detailed stuff with proper close up HD photos you know and downloads and all that stuff it will be over on you to me there you go I like her she's cute I'm going to put a little bit of pink back in this one cheek here I'm also going to be updating my website and hopefully the Yahoo change over to the new company it went well this weekend and I'll be able to do that you to me is spelled U D M E Y and it's an online teaching website and I'll have there's a free well I don't know right now soon there will be the free Hannah Montana course will be back up on there live I don't know if you all remember when I did that with Claudia Rossi where we did the alteration of the Hannah Montana book U D as in dog M E Y dot com I'll have links on my website Gene to be Aaron's dot com as soon as I have everything ready I'm going to be adding a class page including yeah that's it including um University I've got a lot of classes over there I'm going to have some classes over it you to me um and um then there'll be another and there'll be links like for each class if I can do it like for each individual class will take you right to that class um and then also um I'll have a link um for merchandise for different listings for different merchandise and then at the bottom will be the different stores so um and yeah so the Hannah Montana book free you can see it of course on YouTube it's on YouTube but if you don't want to if you don't want it there it is also over on you to me and I'm going to see if I can even make it downloadable for you all but you can't do on YouTube so now I'm just going to neutralize the back a little bit of course not completely I like some of these colors that are going on but it's a little bit distracting with the face so we want to just kind of neutralize her a little bit I like that you can see some of the like music notes from the paper underneath through her neck and you can see some of the paper right here I love that I've got my baby wipe here handy so I can use that to spread the paint around and kind of smooth the lines out I just took my white and I mixed it with some of the brown and some of the other colors I had going on here on my palette I will still be teaching with crazy island university this next year we're getting ready to release journal in crazy island style 2016 there'll be some commercials coming out for that soon I'll let you all know I'll be posting that to YouTube when it's ready thank you I really encourage you all to go out there and try you know doing different kinds of artists faces and trying their techniques and giving a shot but then using what you've learned to come up with something that's uniquely your own that you can really say this your style no matter what class I take now my style of face shows through this is a pre-jessoed little four inch canvas these are coming in two pack for I think $5 hobby lobby and of course I use a coupon so I get them for you know 40% off so I'm going to give her a little bit of a tank top here she's cute now you can make her pop out even more with the stabilo pencil so you know just because you want to if you maybe you want to consider yourself primarily a painter doesn't mean that you can't you know use anything else on your canvases I want to put a little color on the edges of these other colors and this is a wrapped canvas around the side so it's got a little bit of an edge around the side which I kind of like there we go I like that so let's take our stabilo pencil let's actually sharpen it a bit so we have a nice point on it save your stabilo pencil shavings because you can soak them in water in a jar and you can create this kind of inky thing that is fun to paint with and if you think I'm kidding I'm not kidding see stabilo pencil shavings alright so now we've got our pencil all sharpened I'm going to outline her face I'm going to put some lines around her neck and shoulders not too many lines not too dark of lines have a light touch you want to just emphasize and help express her features there we go I like her she's cute does anybody have any questions there we go so whether you choose to do one with features or one without these are really cute fun practice to do they make really great Christmas gifts and wouldn't see even putting them together like that where's my other two wouldn't they be cute just hanging on the wall don't worry Cheryl this is going to be on YouTube and yeah this is acrylic I did the faceless one first and then I did the one with the features in the hour that we've been on and wouldn't I just can totally see a wall in my studio covered with these little paintings I might have to work on that I do have a wall that's about three feet wide by you know the full length of the room and I have the space over the door I you know might have to do some of that little four inch canvases I just you can see a whole wall covered in these I think that would be fabulous yeah like little painting tiles little tiles covering all I love the idea you guys see now I'm gonna have trouble giving these away because they look cute together that's the problem when you create art you know you want I need to make some money at it but then I paint stuff and I don't want to give it away or get or even sell it it's hard to let go of it which would be why I try to like do classes and stuff because that's easier yeah exactly like a quilt only for the wall out of paintings the Lord knows I could not make a real quilt and like ever get it done I started one years ago it's still in my closet I haven't finished it yet alright does anybody have any questions today so look for some changes coming up soon if you're not a member of my Facebook group yet we are about to hit 500 members soon when we hit 500 members and if you're a member of the Facebook group but only if you're a member of the Facebook group you're going to get a free coloring book download for me that's got how many pages does it have I don't even know they're all single-sided these are some never published doodles some that are digital downloads my Etsy shop some that you guys have not ever seen or haven't seen in a long time and I filled the whole book with them and this will be a free digital download when we hit 500 members but you have to be a member of my Facebook group so if you're not yet you should go over there and join tell your friends I may later sell them in my Etsy shop I haven't decided yet but I won't be doing that until after you all get your free copy and I wanted to do this instead of doing it like one giveaway to one person I wanted everybody to get something so this is going to be that something we have a couple minutes I'm going to sit here and you guys can look at the cute paintings if you have any questions let me know I know right it's a good idea thank you to my admin slash assistants and friends Jerry Bellini, Cindy, Utter and Michelle Mitchell because they have been a huge help with the group and with coming up with ideas for next year and encouraging me to get off my butt and get it done so and I can use them as a sounding board too so which is fabulous and they've helped a lot so there you go, life of art and self-expression I'm loving this you guys now I'm going to have trouble giving them away I've got two more, two more I'm going to have to we're going to have to work on that you guys I'm going to have to hang them up I have a fantastic crew in the group I actually do very much so and you guys haven't heard me say this yet I'm going to be doing my group groupies which it kind of happened by accident but I thought calling you all groupies was kind of funny and cute and sweet and all at the same time so you groupies are not too bad either we're all very supportive and I love that we have a lot of men participating in the group which is fabulous and you do not see that in other art groups not the way we've had it in our group a life of art and self-expression not only do I want to welcome all the men to this broadcast and to the group but I thank you all for being there and participating I think it's wonderful that you all feel safe enough to do that thanks I love you all back it's been just as good for me as it has been for you guys believe me alright it is 11 o'clock we have an awesome group of people so invite your friends when we hit 500 that's a good idea Mark we're going to have to post about this Mark in the group I think this is something that we should post about in the group because this is a really great idea alright I'm sorry I'm reading you guys posts oh Tara hey welcome so it's 11 o'clock we've been on for an hour we did these two little face canvases today last week we did a sunflower and before that we did the happy trees alababras we got two more of these little canvases so if we have time before Christmas hits we'll be doing distractions or those of us with anxiety disorder and maybe compulsive issues say ooh squirrel anyway I have two more of these little canvases so we will be trying to get two more of these little live demos of canvases in before Christmas I have more of these to do if I'm going to really do them for gifts so if I run out of time to do live episodes I may do some of them on YouTube so watch for that and I've got a bunch of stuff today to film for YouTube so you all have a great day the sunflower is on YouTube just Google my name go to YouTube and search my name Gina B. Arons or put it in Google I'll show up everywhere I've been on the internet too long now I'm everywhere I can't hide from anybody both of these are on YouTube so the original Periscope Hop that I did this on with Cinnamon Cooney and Susan Hiles where we celebrated Bob Ross's I did this one and then I did this sunflower one which is also on YouTube and these all say Periscope videos all the titles start out with saying recorded live from Periscope or something about Periscope in the title so that's a way to know which ones are which and I'm thinking today as I'm talking to you maybe I should put all the Periscope videos in their own playlist what do y'all think about that because that might be an easy way to find them these all should be under well these three not this one but these should be under Monday with DecoArt too yes see Mark says yes okay Mark you know sometimes it's good to get a guy's opinion and Mark somebody other than my husband who just looks at me like I'm crazy he loves me but he thinks I'm nuts I am nuts but you know alright I really love this okay you guys we're gonna have to do something with this I'm seeing this I might have to photograph these even for the group page I love you guys too have a great day join the Facebook group a life of art and self expression if you can find the link to it on my website jeanabearans.com there will be a free giveaway coming up soon thank you so much I try to make them interesting and um something you all want to see um I don't know how to be anything but me so this is just me I'm not putting on errors or anything else so it's just me I got asked about that recently I don't know how to pretend to be somebody else and I'm thinking about going back to you stream but I definitely need admin help because I can't see the chat ever so um but I'm thinking for the new year we need to do you string once a month because not everybody does periscope so um that's something else I'm working on and I better write it down because I'm gonna forget again alright you all have a great day have a great week and what's what do we say then do something nice for yourself because you deserve it I'll see you later you stream is another live broadcasting site that you actually can see from um a desktop an ipad a phone anywhere and um it's just it's a little trickier periscopes easy so that's why I do periscope message me about it in the group tag me and I'll explain it to you bye guys talk to you later


Okay, so since we just did that lecture on this equation, c equals nu times lambda, let's do a problem on it. So what's the frequency in hertz of a gamma ray with a wavelength of 3.56 times 10 to the negative 11 fields? Let's write it down that way. So this is something you're going to have to remember this equation in this constant. So what are we looking for? It's a frequency, right? So we're going to have to rearrange this equation to isolate the variable frequency in order to do that. We get nu equals the speed of light over lambda. So we have the speed of light here, 3.0 times 10 to the negative 8 meters per one second. And we know the wavelength. So this one's pretty easy. Again, like you said, we didn't have to invert anything. So notice this is the same thing as saying cancel out your units like I do in this problem, this one. So of course this is going to go to 3.56. So I got, hopefully you got, 3.43 times 10 to the 18 per second, remember? And remember what we said about these per seconds? It means hertz. So the answer is going to be 8.43 times 10 to the, it's the frequency of this gamma over ray with this wavelength of 3.56 times 10 to the negative 11 meters is 8.43 times 10 to the 18 per second. Okay, is everybody okay with that? So notice here, one other thing I guess we should notice, real small wavelengths, right? Very, very tiny. So the frequency should be very big. Everybody okay with that? Any questions on this one?


Welcome to George H. Smith's Excursions into Libertarian Thought, a production of Libertarianism.org and the Cato Institute, narrated by James Foster. The Philosophy of the Declaration of Independence Part 1 On June 7, 1776, the Virginian Richard Henry Lee introduced the following resolution on the floor of the Second Continental Congress that these United Colonies are and of right ought to be free and independent states that they are absolved from all allegiance to the British Crown and that all political connection between them and the state of Great Britain is and ought to be totally dissolved. After considering this resolution twice, June 8 and 10, Congress postponed further consideration until July 1. Although the resolution was certain to pass, unanimous ratification by the colonies was wanted and for various reasons this was not possible until some glitches had been worked out. Lee's resolution for American independence passed on July 2, not July 4. This prompted and excited John Adams to write to his wife Abigail. The second day of July 1776 will be the most memorable epoch in the history of America. I am apt to believe that it will be celebrated by succeeding generations as the great anniversary festival. It ought to be commemorated as the day of deliverance by solemn acts of devotion to God Almighty. It ought to be solemnized with pomp and parade, with shoes, games, sports, guns, bells, bonfires, and illuminations from one end of this continent to the other from this time forward forevermore. On June 11, Congress appointed a committee of five to draft a declaration. Thomas Jefferson, John Adams, Benjamin Franklin, Roger Sherman, and Robert R. Livingston. Events became somewhat murky after this point because Jefferson and Adams provided different accounts in later years. An 88-year-old Adams claimed that he and Jefferson were appointed as a subcommittee to prepare a draft after which Adams persuaded Jefferson to write the document. An 80-year-old Jefferson disputed this account. He denied that a subcommittee had ever been formed, claiming instead that the entire committee unanimously pressed on myself alone to undertake the draft. A more serious discrepancy between the accounts of Adams and Jefferson pertains to how the declaration was actually drafted. In his autobiography, 1805, Adams recalled that the Committee of Five held several meetings, during which an outline of the declaration was drawn up to serve as a guide for the draftsman. Jefferson gave no indication of such an outline, suggesting instead that he had written the declaration from scratch. It was only after he had completed the original rough draft that Jefferson submitted the document to Adams and Franklin separately, soliciting changes that he later described as two or three short and verbal alterations. But Jefferson continued, even this is laying more stress on mere composition than it merits, for that alone was mine. The rough draft to which Jefferson refers is one of the most fascinating documents in American history. In 1945, Julian P. Boyd, the Declaration of Independence, the evolution of the text, page 26, said of it, there can scarcely be any question but that the rough draft is the most extraordinarily interesting document in American history, for it embodies in its text and in its multiplicity of corrections, additions, and deletions, all or almost all, of the declaration as it was at every stage of its journey, from its origin in the parlor of Graff's home, to its emergence in full glory as the official charter, as the authenticated charter of liberty to the American people. For those who wish to understand the political philosophy of the declaration, the significant part is the famous second paragraph. The first part of the second paragraph, as painstakingly reconstructed by Carl Becker in 1922, the Declaration of Independence, a study in the history of political ideas, originally read, we hold these truths to be sacred and undeniable, that all men are created equal and independent, that from that equal creation they derive rights inherent and inalienable, among which are the preservation of life and liberty and the pursuit of happiness, that to secure these ends, governments are instituted among men, deriving their just powers from the consent of the governed, that whenever any form of government shall become destructive of these ends, it is the right of the people to alter or abolish it and to institute new government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to affect their safety and happiness. We have here a brilliantly concise statement of what historians call real or radical wig ideology, a libertarian political philosophy commonly associated with John Locke. But before I delve into this philosophy, I want to comment on a point of historical trivia. The declaration we know today refers to unalienable rights, but Jefferson used the word inalienable. Jefferson did not make this change, nor does the change appear to have been made by Congress while it was considering the draft submitted by the Committee of Five. So who made this change and why? We don't know. Unalienable first appears in John Dunlop's initial printing of the declaration, July 5, which was inserted in the rough Journal of Congress. It also appears in the corrected journal and in the engrossed parchment version, which was signed by delegates on August 2nd, contrary to the later recollections of Jefferson and Adams, no signing occurred on July 4th. Carl Becker suggested that John Adams may have been responsible for the change. Adams was one of the committee which supervised the printing of the text adopted by Congress, and it may have been at his suggestion that the change was made in printing. Julian P. Boyd, editor of the massive Princeton edition of the Papers of Thomas Jefferson, proposed a different theory. This alteration may possibly have been made by the printer, John Dunlop, rather than at the suggestion of Congress. Fortunately for my purpose here, this minor mystery is of no consequence. Both inalienable and unalienable were used throughout the 18th century. They were merely variant spellings of the same word. Unalienable appears to have been more common. Far more significant is why Jefferson felt the need to specify inalienable rights at all rather than referring simply to natural rights, inherent rights, and so forth. Inalienable or unalienable rights were regarded as fundamental corollaries of man's nature, especially his reason and volition, so these rights could never be surrendered or transferred to another person, including a government, even with the agent's consent. A man can no more transfer his inalienable rights than he can transfer his moral agency, his ability to reason, and so forth. This means that inalienable rights could never have been transferred to government in a social contract, so no government can properly claim jurisdiction over them. This argument from inalienable rights was important because of an ambiguity in traditional social contract theory. The social contract was more of a theoretical construct than a historical reality, so disagreements inevitably raged over which rights had been delegated to government and which rights had not. After all, no legitimate complaint can be made about the violation of a right if a government has gained proper jurisdiction over that right in the social contract. Government, for instance, cannot function without money, so the transfer of a minimal amount of property to government, collected in the form of taxes, was commonly seen as the prime example of a right that has been alienated in a social contract. According to this approach, legitimate disagreements may occur between subjects and rulers when inalienable rights are involved, but no such disputes are justified over the question of inalienable rights. Government cannot claim any jurisdiction over such rights because inalienable rights, by their very nature, could never have been transferred to government in the first place. Therefore, there can be no excuse for the violation of inalienable rights. This is the crucial bright-line test that enables us to distinguish the incidental or well-intentioned violation of rights, which even just governments may occasionally commit from the deliberate and inexcusable violations of a tyrannical government. We thus see why Jefferson focused on inalienable rights in order to fasten the charge of tyranny on the British government. The violation of inalienable rights was a defining characteristic of a tyrannical government, and only against such a government is revolution justified. Although this basic argument can be found in John Locke's Second Treaties of Government, Locke never actually used the word inalienable or unalienable in regard to rights. We do find this terminology, however, in an early book by the Scottish and Lockean philosopher Francis Hutchison. In an inquiry into the original of Our Ideas of Beauty and Virtue 1725, Hutchison discusses an important difference of rights according as they are alienable or unalienable. In order for a right to be alienable, it must be possible for us, in fact, to transfer our right. Some rights, such as the right of private judgment, cannot be transferred because they flow directly from our nature as moral agents, and we cannot transfer our faculties of volition and judgment to other people as we might transfer a piece of external property. In the same way Hutchison continues, a direct right over our lives or limbs is not alienable to any person so that he might, at pleasure, put us to death or may must. Hutchison clearly states the political implications when inalienable rights are violated by government. All human power or authority must consist of a right transferred to any person or council to dispose of the alienable rights of others and that consequently there can be no government so absolute as to have even an external right to do or command everything. For wherever any invasion is made upon unalienable rights, there must arise either a perfect or external right of resistance. Unalienable rights are essential limitations in all governments. As indicated by Hutchison's mention of perfect and external rights, the doctrine of inalienable rights presupposed a rather elaborate theory of natural rights. Space does not permit a discussion of that theory here. I will discuss it in detail later in a separate essay on natural rights. Suffice it to say that the distinction between alienable and inalienable rights had become commonplace by the time Jefferson wrote the Declaration in 1776. It is found in the standard works on natural law familiar to 18th century Americans, such as that written by Jean-Jacques Belmaquis. The Principles of Natural and Political Law, 1747-1751. Among American writers, the distinction between alienable and inalienable rights was frequently invoked by defenders of religious freedom. Perhaps the best example of this was published in 1744 by the dissenting minister Elisha Williams. The Essential Rights and Liberties of Protestants, a seasonable plea for the liberty of conscience and the right of private judgment in matters of religion without any control from human authority. After designating freedom of conscience as an inalienable right, Williams explains, This I say, I take to be an original right of the humane nature and so far from being given up by the individuals of a community and a social contract that it cannot be given up by them if they should be so weak as to offer it. Once it follows, the rights of conscience are sacred and equal in all, and strictly speaking, inalienable. A man may alienate some branches of his property and give up his right in them to others, but he cannot transfer the rights of conscience unless he could destroy his rational and moral powers or substitute some other to be judged for him at the tribunal of God. Although the appeal to inalienable rights first arose in the context of religious freedom, it was quickly extended to spheres other than religion as we find in Jefferson's appeal to the inalienable rights of life, liberty and the pursuit of happiness. As I explained in my first Libertarianism.org essay, this was one of the most significant developments in the history of Libertarian thought.


As Salaamu Alaikum, welcome to lecture number 41 of the course on statistics and probability. Students, you will recall that in the last lecture, I discussed with you, internal estimation and hypothesis testing regarding mu 1 minus mu 2 based on the t statistic and the t distribution and that situation was valid when the populations were normal, the standard deviations of the populations were unknown, but equal and the sample sizes were small. Towards the end of the last lecture, I began the discussion of the application of the t distribution in the case of paired observations. Let us continue that discussion and let us go back to the example that I quoted at the end of the last lecture. As you now see on the screen, 10 young recruits were put through a strenuous physical training program by the army, their weights were recorded before and after the training with the following results. For recruit number 1, the weight before the training was 125 pounds, whereas after the training it was 136 pounds. Similarly, we have the figures for all the other recruits. Using a level of significance of 5 percent, would you say that the program affects the average weight of the recruits, assume the distribution of weights before and after the training to be approximately normal? Students, as I mentioned last time, this is a case of pairing and we can say that this is natural pairing. We are interested in finding out that, is there any difference in the weight of the training or not? As I was saying last time students, the statistic in this particular case is t equal to d bar minus mu d over sd over square root of n. So, we are going to compute the differences in the weights before and after the training. So, as you now see on the screen, if we regard the weights after the training as x1, the weights before the training as x2 and we define d as x1 minus x2, then the 10 differences come out to be 136 minus 125 equal to 11, 201 minus 195 equal to 6, 158 minus 160 equal to minus 2 and so on. Students, each of this differences I have, you should regard them as a sample of differences out of a population of differences. If we do not have 10 recruits, if we do not have 10,000, if we had 1000s and 1000s of recruits, the entire population would have been there. Theoretically, we can say that if we had spent every one of them from this physical training and we had recorded the weights before the training and after the training for all of them, then we could have found differences of this type for all of them and that would be a large population of differences. These 10 differences can be regarded as a random sample out of that population. Another very important point to note is that if both x1 and x2 are normally distributed, then the difference d which is x1 minus x2 that will also be normally distributed. This is because of a basic mathematical property of the normal distribution and the property says that if x and y are normally distributed, then x plus y or x minus y will also be normally distributed. So, a x y or x1, x2 point is that if those two variables are normally distributed, then the difference of these new variables is also normally distributed. In this problem, x1 is the weight after the training, x2 is the weight before the training. So, weight to parhal approximately normally distributed. Therefore, we can say that this population of differences x1 minus x2 is also normally distributed. This is very important because if the parent population is normal, its standard deviation is unknown or sample size is small, then we apply t-statistic. This is what is happening. We are assuming that we have a random sample of differences from a normally distributed population of differences and of course, the standard deviation of the population which I may call sigma d is unknown or our sample size, it is small and we had only a sample of 10 recruits. So, all those assumptions and conditions are being fulfilled and this is why in this particular case, we will be applying the t-statistic which you now see on the screen. t is equal to d bar minus mu d over sd over square root of n. As I have said two or three times, this is similar to the statistic that we had earlier which was t is equal to x bar minus mu over s over square root of n. This statistic we had used earlier, if I wanted then I could have read it this way, t is equal to x bar minus mu x over sx over square root of n. If you replace x by d, then you get the one that we have now, students, they are one and the same. There is nothing wrong with that, that is absolutely correct, because when we were talking about x variable, then we used to compute mu or s. After all, mu that was the mean of the population of the x values and so, there was nothing wrong with saying mu x. Similarly, sx would have been the standard deviation, sample standard deviation of the x values that we had taken in the form of a sample from that population. So, baat phir wohi students ke aap basic pattern ko dekhye, aur dekhye ke wohi baat repeat ho rahe jo pehle ho rahe thi. Now that we have the statistic in mind, I think we should go to the six steps that we have in any hypothesis testing procedure step by step according to a methodical approach. The first step of course, is the formulation of the null hypothesis and the alternative. And what is the null hypothesis in this particular example? So, students hum ye jaana chaatein ke ye jo physical training program hai uska weight pe koi asar patta hai yaani to null kya hoga? Ye hi hona chahiye na that there is no difference in the weight before the training and after the training, yaani us program se koi farat nahi patta as far as the weight is concerned. And what will be the alternative that it does make a difference? So, the alternative says that mu 1 is not equal to mu 2. In this case 1 is standing for the weight after the training, 2 is standing for the weight before the training and what we are saying is ke wo baraabar nahi hain, iska matlab ke kuch fark pat jata hain, ho sakta hai, kam ho jaata ho, sakta hai, jada ho jaata ho, fark pad hain. So, students issi baat ko hum iss tarasi bhi toh kya sakta hai na, ke null hypothesis ye hain ke mu 1 minus mu 2 is equal to 0 and the alternative is that mu 1 minus mu 2 is not equal to 0. As you now see on the screen mu 1 minus mu 2 is equal to expected value of x 1 minus expected value of x 2 iss liye ke expected value ka matlab hi mean hota hai. And this can be written as expected value of x 1 minus x 2 iss liye ke ye toh basic algebraic equation hai that e of x minus y is equal to e of x minus e of y. So, mu 1 minus mu 2 equal to 0 means expected value of x 1 minus x 2 equal to 0 or in other words expected value of d equal to 0 or in other words mu d equal to 0 and students this is exactly our null hypothesis in terms of the variable d H naught mu d is equal to 0 and H 1 mu d is not equal to 0. The next step is the level of significance and as you now see on the screen in this problem we set it to be the usual level 0.05. The test statistic under H naught as mentioned earlier is t is equal to d bar minus mu d over s d over square root of n, but since our null hypothesis says that mu d is equal to 0. Therefore, t can be written as simply d bar over s d over square root of n. Now, it can be mathematically proved that this particular statistic follows the t distribution with n minus 1 degrees of freedom exactly similar to what we had when we were considering the variable x and testing for the mean of that variable. The fourth step is the computation of the statistic and as you now see on the slide in order to find t we first have to find s d and to find s d we need to have a column of d square which you see in the last column of the table that you have in front of you now the d square values are 121, 36, 4, 169 and so on. Substituting the sum of this column and the sum of the earlier column in the formula of s d square we obtain s d square equal to 50.23 so that s d comes out to be 7.09. Of course, d bar is very easily found by simply dividing the sum of the d column 47 by 10 and that comes out to be 4.7. Hence, the computed value of our test statistic in this problem comes out to be 2.09 students. Obviously, we would like to compare this value with the critical value and what is the situation now? Is it a one-tailed or a two-tailed test? Of course, it is a two-tailed test, that mu d is not equal to 0. Either mu d is less than 0 or mu d is greater than 0 or less or greater, dono sign involve hogay. So, both the tails of our t distribution are involved and therefore, we will have to divide our level of significance 5 percent by 2 half of it in the left tail half in the right. So, we will have 2.5 percent area to the right of the critical value that we will have on the right tail and 2.5 percent area to the left of the critical value that we will have on the left tail. Now, how do you find the critical value? Degrees of freedom n minus 1, we have 10 recruits to 10 minus 1 means 9 and so, when we look in the t table against 9 degrees of freedom under 0.025, what do we get? As you now see on the slide, the critical values come out to be 2.262 and minus 2.262. Interesting point. In order to test mu 1 equal to mu 2, degrees of freedom mu 3 n 1 plus n 2 minus 2. 10 plus 10 minus 2, 10 before the training, 10 after the training values 20 minus 2 18. Why did I not use 18 degrees of freedom students? The reason is as I explained earlier, ab aap isko ek population of these, yani differences tasavur karein aur yeh samjhein ke ish population me se you have drawn one sample of size 10 in this case, a sample of these. Yeh do alagalak sample, jis ke liya hum kaheen ke n 1 plus n 2 minus 2, yeh ustra ki situation nahi hai. This is the case of paired observations, jaha pe hum isko ish dosre tari khe se treat karte hain, jasa kum hai aaps ke saath baat karein. That is the last step, the conclusion. Our computed value of T came out to be 2.09 and the critical values are plus minus 2.262. Isle saaf zahire ke humare value acceptance region ke ender fal karein and therefore, we can accept H naught. Isko matlabhi hua that this data does not provide evidence to conclude that this particular physical training program affects the weights of those recruits. Of course, we are not talking about any particular individual, but we are talking on the average. Let us consider one more example on paired observations. As you now see on the slide, the following data give paired yields of two varieties of wheat. Each pair was planted in a different locality. The values are that for locality number 1, the yield for variety 1 is 45, whereas the yield for variety 2 is 47. Similarly, for locality number 2, the yield of variety 1 is 32 and the yield of variety 2 is 34. Isi tarase humare pas baqi figures majuudhe. Now, we would like to test the hypothesis that on the average, the yield of variety 1 is less than the yield of variety 2. Also in this problem, we are required to state the assumptions that are necessary to carry out the test that we are going to carry out. In addition, there is a very interesting question. How can the experimenter make a type 1 error and what are the consequences of his doing so? Next, isi tarase hum ye bhi jaan na chaathe ke, how can the experimenter make a type 2 error and what are the consequences of his doing so? In addition, we would like to compute the 90 percent confidence interval for the difference in the mean yield of the two varieties. Students, sabse pehle aap ye note karein that this is again a case of paired observations. Humare pas das mukhtalif farms hai aur har farm me humne aadhe me variety 1 ko boya hai aur aadhe me variety 2 ko. Isli ye soil is common aur ab agar pehle baar me kui faar aar hai. So, it is not because of soil or any other extraneous factors which could affect the yield. It is simply the difference in the varieties that is producing the difference in the yield and this is exactly what we are wanting to measure. So, if we are satisfied that this is the way we should treat this problem, then what are the assumptions in order to conduct the test? As you now see on the screen, we will be assuming that the differences in the yields of the two varieties in the 10 farms that we have, these are a random sample from the population of differences and the population of differences is normally distributed. This means that we can think that if we talk about 100,000, 10,000 farms instead of 10,000 farms, in every farm we give half variety 1 and half variety 2. So, we have a population of yields for variety 1 as well as for variety 2 and after that if we compute the differences then we have a population of differences. This population may say we are drawing a random sample of size 10. All right students, what is it that we are wanting to test? Statement ye thi ke variety 1 ki yield jo hai on the average it is less than variety 2 ye hum test karna chaatein. Dekhye iss ki andar less than ka sign hai. Equal ka sign iss me nahi aata iss ka matlab hai ki this will be in the alternative hypothesis. Agar hum variety 1 ke liye subscript 1 use karein or variety 2 ke liye subscript 2, then what are we saying? We are saying mu 1 is less than mu 2. This comes in the alternative hypothesis and what is the null hypothesis then? mu 1 is greater than or equal to mu 2. Lekin agar hum in hypothesis ko translate karein into those which are in terms of d, then as you now see on the screen the null hypothesis is mu d is greater than or equal to 0 and the alternative mu d is less than 0. The second step is the level of significance and let us keep it as 0.05 the usual level that we take. The third step is the test statistic t is equal to d bar minus mu d over s d over square root of n and the fourth step is to compute this statistic carrying out the computations just as in the last example our d bar comes out to be minus 2.8 s d square is equal to 1.7333 so that t comes out to be minus 6.71. Now the critical region lies on the left tail of the distribution and looking under 0.05 in the t table against 9 degrees of freedom the value is 1.833 but because we have the left tail in our mind therefore we say that the critical value is minus 1.833. The last step of course is the conclusion. Our value is minus 6.71 which is far out in the left tail and therefore we reject the null hypothesis and therefore we conclude that there is sufficient evidence for us to say that mu 1 is less than mu 2. That means variety 1's yield on the average it is less than the yield of variety 2. Students you will recall that there was a very interesting question in this problem. How can the experimenter make a type 1 error and what will be the consequences of his doing so? You remember type 1 error means that h naught is actually true but you reject it. In this problem h naught kya tha mu 1 is greater than or equal to mu 2. That means mu 1 the mean yield of the first variety is either more than or at least equal to the yield of variety 2. To agar yeh such ho aur ham it se reject karne aur ham kahe variety 1 ki yield kam hai variety 2 se to is aisa error karne ke consequences kya honge? Students first ki jay ke variety 1 joh hai that is less expensive than variety 2 aur ham kahe ke jee expensive to kam hai lekin uski yield bhi kam hai lehaaza we should not take that one we should be buying the other one and showing the other one. But then students will be not be wasting money is liye ke dar asal to uski yield less nahi hai asal me to h naught is true aur agar wo inexpensive hai to phir to hame wohi lene chahiye thi na aap ko mai ke is maam le pe gaur ki jay. This is how you link the mathematical theory with real life and if you pay attention to it it can be very interesting. The other question was how can the experimenter made a type 2 error? Type 2 error kya hota hai? Ke joh nal hypothesis hai that is actually false. But you accept it because of your data being that way to is problem me nal hypothesis ye hai ke mu 1 is greater than or equal to mu 2. First ki jay ke ye asal me galat hai. Asal me mu 1 is less than mu 2 variety 1 ki yield kam hai variety 2 se on the average. Lekin ham agar accept karne h naught ko which is actually false. To ham kainge ke neji variety 1 ki yield kam nahi hai variety 2 se. To aisa karne se nuksaan kya hoega? Aisa karne se nuksaan ye hoega students ke ham jo isafa kar sakte thi payada war me by using variety 2 wo ham nahi karir sakenge because of this error that we have committed. So, this is the kind of situation that we deal with in hypothesis testing. Now, the last part of the question was construct a confidence interval for mu 1 minus mu 2 and how do we proceed with this problem? Aapko yaad hai na ke ye wala problem toh bad observations kahe. To iska matlab ye hua ke ju hamara confidence interval hai that also has to be in that manner as you now see on the screen. In the case of paired observations the confidence interval for mu 1 minus mu 2 in other words the confidence interval for mu d is given by d bar plus minus t alpha by 2 n minus 1 degrees of freedom multiplied by s d over square root of n. Once again note ki jay exactly the same formula that we had in the first instance when we were trying to construct a confidence interval for mu the mean of our x variable. Uswa formula kya tha? x bar plus minus t alpha by 2 n minus 1 degrees of freedom into s over square root of n or ye formula bilkul wesa hi hai. The only difference being that our variable now is not x, but d. So, let us apply this in this problem as you now see on the screen d bar is equal to minus 2.8, s d is 1.32 and n is equal to 10 and therefore our confidence interval is minus 2.8 plus minus t alpha by 2 at 9 degrees of freedom into 1.32 over square root of 10. As noticed earlier the value of t alpha by 2 that is t 0.025 at 9 degrees of freedom ab ye jo t alpha by 2 ki baat horei hai students note ki jay ke ham chaate hai ke ham 90 percent confidence interval nikale. Iska matlab ye hua that 90 percent area in the middle 5 percent to the left 5 percent to the right. So, having a look at the area table of the t distribution of course the t value comes out to be 1.833 just as in the case of hypothesis testing that we did a short while ago. Therefore, putting the value 1.833 in the formula our confidence interval comes out to be minus 3.565 to minus 2.035 and rounding these figures the 90 percent confidence interval for mu 1 minus mu 2 is minus 3.6 to minus 2.0. As you can see the values are negative and this means that mu 1 is less than mu 2. Zahire agar mu 1 mu 2 se kam ho ga tabhi mu 1 minus mu 2 negative eigena alright students. We have conducted a number of tests and constructed a number of confidence intervals based on the t distribution.  Isse pehle you will recall that we were testing about mu on the basis of the Z statistic and also when we were doing the Z statistic we were testing about p 1 p 2 and also constructing confidence intervals regarding proportions. Another very important quantity that we might wish to estimate is the variance or the standard deviation of our population. Agar ham sigma square ya sigma ke baare mein statistical inference karna chahi then what will be the procedure? Students you will be interested to know that there is another distribution called the chi square distribution and this is the one that will enable us to do statistical inference for sigma square the variance of the population. So before I do the application of the chi square distribution in real life situations let me first define this distribution for you in a formal manner. As you now see on the slide the mathematical equation of the chi square distribution is f of x is equal to 1 over 2 raise to nu by 2 into the gamma function gamma of nu by 2 and this whole quantity multiplied by x raise to nu by 2 minus 1 multiplied by e raise to minus x by 2 and this whole equation is valid for x lying between 0 and infinity. All I would like you to do is to note that it has only one parameter represented by nu and also note that x ranges from 0 to infinity or its properties. Let us have a look at the equation one more time f of x is equal to 1 over 2 raise to nu by 2 gamma of nu by 2 x raise to nu by 2 minus 1 e raise to minus x by 2. Ab de kray hei ke sirif nu hei wo quantity hei which is the unknown quantity and which is the one lone parameter of the chi square distribution. Now coming to the properties of the chi square distribution first and foremost we can say that it is a continuous distribution ranging from 0 to infinity as is evident from its equation. And as far as the shape of the distribution is concerned the parameter nu determines the shape, nu is known as the degrees of freedom of the chi square distribution and there is a different chi square distribution for each number of degrees of freedom. As such it is a whole family of distributions just as we had in the case of the t distribution or the normal distribution or for any other distribution. The curve of the chi square distribution is positively skewed, but the skewness decreases as nu increases. Students yeh ju point abhi main aapko diya iska matlab yeh hua ke jay se jay se aap degrees of freedom barhate chale jate hi uski jo skewness hei that becomes less and it looks more and more like a normal distribution. The next property as you now see on the slide the diagram that you have in front of you now in this we have drawn three chi square distributions one for two degrees of freedom one having six degrees of freedom and one having ten degrees of freedom and you can see that whereas the chi square distribution with two degrees of freedom is extremely skewed the one having ten degrees of freedom is much less skewed and looks much more like a normal distribution. The next property pertains to the mean of the chi square distribution and it has been mathematically proved that the mean of the chi square distribution is equal to nu the number of degrees of freedom. As far as its variance is concerned it is equal to two times nu iska matlab yeh hua ke agar hum ten degrees of freedom wali chi square distribution ki baat karene to uski jo mean value hei that is equal to ten or uska jo variance hei that is equal to two times ten that is twenty yeh ni agar hum iska square root leh square root of twenty how much is that is it four point something yes then the standard deviation the spread of this distribution is square root of twenty. The next property is also very interesting as you now see on the slide the moments about the origin for the chi square distribution are as follows mu one dash is equal to nu mu one dash of course is the same thing as the mean because after all do you not remember that the first moment about the origin in other words the first moment about zero is exactly the same thing as the mean also mu two dash is equal to nu into nu plus two mu three dash is equal to nu into nu plus two into nu plus four and mu four dash is equal to nu into nu plus two into nu plus four into nu plus six dekhah aapne kis kadar hubsureth formulae it just goes on in a systematic pattern. But students we are more interested in the moment ratios and as you now see on the slide the first moment ratio beta one comes out to be eight over nu and the second one beta two comes out to be three plus twelve over nu. Students aap hui aadhe abhi thori dekhah lee main aapse kaha that as the degrees of freedom increase the skewness of the chi square distribution decreases and it becomes more and more like the normal distribution is baat ko in moment ratios kis aath relate ki jai jo abhi abhi aapne aapne present kiye gaye. Since beta one is equal to eight over nu isn't it obvious that if nu tends to infinity beta one will tend to zero and also since beta two is equal to three plus twelve over nu as nu tends to infinity beta two will tend to three plus zero and that is three and students do you not remember that for the normal distribution beta one is equal to zero and beta two is equal to three. Hence what we said earlier regarding the shape of the chi square distribution is validated by the moment ratios. Students having discussed the basic properties of the chi square distribution let us now begin the discussion of its role in estimation and hypothesis testing. As I said earlier we can do hypothesis testing or estimation regarding the variance of our population on the basis of the chi square distribution. Let me explain this point with the help of an example. Suppose that an aptitude test has been devised in such a way that it carries a total of 20 marks and suppose that this test is administered on a large population of students and when the result comes out we find that the marks of the students are normally distributed. Now a random sample of size eight is drawn from this normal population and the sample values are nine, fourteen, ten, twelve and so on. We are required to find the 90 percent confidence interval for the population variance sigma square representing the variability in the marks of the students. Let us have a look at the data once again. The marks of the students in our sample are 9, 14, 10, 12, 7, 13, 11 and 12. You can see that these marks are not all the same obviously there is some variation. Now if we talk subjectively, some will say that there is quite a bit of variation. So, obviously we need a proper mathematical way of doing it and as you now see on the screen, if we are interested in constructing a 90 percent confidence interval for sigma square it is given by summation x minus x bar whole square over chi square 0.05 at nu minus 1 summation x minus x bar whole square over chi square 0.05 n minus 1 degrees of freedom. This is the lower limit and the upper limit is summation x minus x bar whole square over chi square 0.95 n minus 1 degrees of freedom. The next slide shows what we mean by chi square 0.05 and chi square 0.95. The value chi square 0.95 indicates that value on the x axis. The area to the right of weight is 95 percent of the total area under the chi square distribution. Similarly, the value chi square 0.05 is that point on the x axis. The area to the right of weight is 5 percent of the total area. As indicated already, the degrees of freedom that we have to use are n minus 1 and in this problem that is 8 minus 1 and that is 7. Now, in order to find the values of chi square we will need to consult the chi square table which you now see on the screen. The very first column indicates the degrees of freedom and the very top row indicates the areas that we would like to have to the right of our chi square values. Hence, in this particular problem if we want 90 percent confidence, then we will be looking against 7 degrees of freedom. Once we will be looking under 0.95 and we find the value to be 2.17 and the other time we will be looking under 0.05, so that we find that chi square is equal to 14.07. Substituting these values in the lower and upper limits, we obtain summation x minus x bar whole square over 14.07 as the lower limit and summation x minus x bar whole square over 2.17 as the upper limit. Now, the question is, what is the summation x minus x bar whole square value? That is very obvious. We have the data and we can find these values either directly or by the shortcut formula. So, as you now see on the slide, in this problem x bar is equal to 88 over 8 because the sum of the values is 88 and therefore, x bar is equal to 11 and substituting this in the formula sum x minus x bar whole square, we obtain 9 minus 11 whole square plus 14 minus 11 whole square plus so on, so that the sum of the squares of the deviations of the values from their mean comes out to be 36. Substituting this number 36 in the lower and upper limits, we obtain 2.56 as the lower limit and 16.61 as the upper limit of our 90 percent confidence interval for sigma square. Students, we have found the 90 percent confidence interval for sigma square. The values are lower limit 2.56 and upper limit 16.61. Now, this seems to be a bit wide. But, if we talk about sigma square instead of sigma, that is, standard deviation, then we should do that and that will give us the confidence interval for sigma. As you now see on the slide, if we do so, then the lower limit for sigma comes out to be 1.6 and the upper limit 4.1. And you can see that this of course, is much narrower than what we had for the variance. But, then do keep in mind that after all the variance was in square units whereas, the standard deviation itself is in the original unit. So, we adopt this method several times. The basic formula is for sigma square, but later we may take the square root and we can then regard it as a confidence interval for sigma. Students, we solved the problem, but the question is how did we achieve this particular formula? Well, it has a derivation similar to the derivation that I convey to you for the confidence interval for mu based on the z statistic. But, I will not be doing the detailed derivation of this particular formula in this course. All I would like you to note is that the basic requirement for this formula to be valid is that the population from which the sample is drawn that population should be normally distributed. Having done interval estimation regarding sigma square, let us now proceed to hypothesis testing regarding the variance of the population. Let me explain this with the help of an example. As you now see on the slide, the variability in the tensile strength of a type of steel wire must be controlled carefully. A sample of the wire is subjected to test and it is found that the sample variance is 31.5. The sample size was n equal to 16 observations. Test the hypothesis that the population variance is 25 against the alternative that the variance is greater than 25. Use a 5 percent level of significance. Students, you will agree that in any production process we want to control the product according to the specifications and the variability that is what we want to control and that is exactly what we have in this particular problem. So, we want that the variability should not be greater than 25 in terms of the variance of the tensile strength. Now, how do we solve this problem? As you see on the slide, the null hypothesis is that sigma square is equal to 25, whereas the alternative is that sigma square is greater than 25. The level of significance is 5 percent and students the test statistic in this particular situation is summation x minus x bar whole square over sigma square which under H naught has a chi square distribution with n minus 1 degrees of freedom assuming that the population is normal. In order to calculate the value of chi square, we note that summation x minus x bar whole square is equal to n times s square and substituting these values in the formula and substituting 25 instead of sigma square, we obtain chi square is equal to 20.16. The next step is the critical region and since this is a right tail test students therefore, we will look against 16 minus 1 that is 15 degrees of freedom under 0.05 and doing so, we obtain the critical value as 25.00. Since our computed value 20.16 is less than 25, therefore, we accept the null hypothesis and we do not find evidence to conclude that the variability in the tensile strength is greater than 25. Students in today's lecture, we discussed the difference between means in the case of paid observations and after that, we began the discussion of the chi square distribution. I would like to encourage you to study these concepts in detail and until next time, Allah hafiz.


The Doki Doki Literature Club is not an SCP, but if it were, how would the SCP Foundation contain it? Sentient artificial intelligence constructs would be worthy of containment in the Foundation's eyes. Luckily, the containment is quite simple. In our scenario, the game would be removed from download platforms as soon as the Foundation got word that the characters were alive. A disinformation campaign would be enacted to convince the general public that the game was never released, simply an urban legend. You may recall a similar containment procedure we enacted called Polybius. Foundation web crawlers would remove conspiratorial posts that refute our story, and agents would be dispatched to amnesticize particularly adamant gamers. Team Salvato, the developers of the game, would be detained and questioned. Their containment, amnesticization, or other fates would be up to the answers they gave regarding their creation of these AIs. Two copies of the game would be kept intact, the testing copy and the backup copy. The testing copy would be stored on a Foundation computer without internet access. This computer would be kept in a faraday-shielded room. Researchers are to relinquish all electronics before entering the chamber. The backup copy would be kept in an isolated data drive and a storage locker. Researchers would begin study by interviewing the Monica entity. In kinder research scenarios, we would continue working with the Monica entity and possibly give it a non-staffed therapist to help it deal with its emotional issues regarding its situation. In colder test scenarios, we would likely have Monica deleted in order to pass the self-awareness on to the other characters in order to gain even more insight. As for the cryptic references regarding Project Libertina, the portrait of Markov, the third eye, etc., well, research continues. Make sure to like and share this video, comment any creatures you would like to see containment procedures implemented for, and remember that patrons of Site 42 get priority for their COMPROX requests. Secure. Contain.


algae are being explored as a potential high yield feedstock for biofuels production due to their significant lipid and carbohydrate production, ability to grow using non-potable water sources and useful biomolecular substrates, lipids. Environmental factors such as temperature, light, and pH, as well as nutrient availability including carbon, nitrogen, phosphorus, potassium, and trace metals, affect growth rate and cellular composition. Understanding synergistic interactions between multiple environmental variables and nutritional factors is crucial for developing sustainable high productivity bioalgae systems essential for commercial biofuel production, with a focus on carbon fixation and partitioning from a biofuels perspective. This article was authored by Ganti S. Morthy, Ruben Michael Sabalos, and Ankita