Welcome to Dare to Dream. This is Debbie Dashinger, a favorite place to be on the planet every week. I feel so blessed to have these conversations and man, you guys are ramping it up on YouTube. So thank you so much for taking the time to submit your comments. I tell you every week I read them, I read them, I respond. I love hearing how this show is changing your life, how the guests are teaching you pieces, showing you things you didn't know before. For those of you who are listening to this in podcast form, but you'd actually like to see what I look like, what my guests look like, come join us and click on subscriptions at youtube.com slash Debbie Dashinger. And you could do the visual too. And that's pretty fun. That kind of amps everything up for us visual people. And also, if you're enjoying the show and conversation, this show has been nominated for People's Podcast Choice Award. Please be sure to leave us a review, right? It's so important. That's how people find our conversations. So I love that you click on. And by the way, this show is doing really well in other countries. I'm on, I get an email every week that tells me where the show is. It's, you know, for some shows, I'm sure it's like the stock exchange. It goes up and down and up and down. But this show really is doing very well. And for those of you who are not listening in the US and listening in other country, I adore you. The world is so small today.  And I'd love, frankly, if you write in two, let me know where you're writing in from. And how's it going? How's the show impacting you in the world that you live in? Well, I want to first thank the sponsor to the show, Dr. Dean here, H-E-E-R and Access Consciousness. I want to thank them for the beautiful work they do out in the world.   Check out their work. They do stellar work all around the world in every country. So it's accessconsciousness.com, as well as Dr. Dean, D-A-I-N, here, H-E-E-R.com. And you can start out real low-level or book or an online course or actually join them at a workshop. And they also do bars, energy work, which I'm a facilitator at, so we can facilitate your healing now. So I have a good show coming up. And I'm excited because Simone Butler is here, and she's a professional astrologer. And she's going to talk to you about how to use astrology for knowing where in the world should I be living? What city, what state, what country? I think that's really cool. And I know so many people today. I was telling Simone earlier that where I go, the people I hang out with all seem to want to know that. Or if I bring it up and passing, everybody's like, where can I get that done? So I thought, let me bring on the person who can tell you where you can figure these things out. She can help you do that. And she'll be on just a little bit later. And who am I? What do I do out in the world? Well, I work with spiritual entrepreneurs who are ready to write their book and make it into a page turner. I coach you to do that. I've also got a company that takes authors to a guaranteed international bestseller status. And I teach the ultimate visibility formula. I work with amazing clients to show them how they can be interviewed on radio and podcasts in 60 days or less. But not just where to be interviewed, I give you all the shows, but also how to be exquisite while you're on the microphone or camera. I myself have been interviewed on over 1000 media outlets. I know all the ins and outs and how to build influential relationships and how to actually get results, not just be interviewed, but get results, sell out workshops, books, get clients when you're being interviewed. Join my class at debid.net, love to have you. Our next class is starting in about six weeks. You want to sign up now and just check out the testimonies. They're pretty stellar. Do you know how to set up your home or the best place in the world for you to live? Well, my guest today, Simone Butler, is an expert astrological guide. She's got more than 30 years experience in helping people find their purpose and passion. She began her career as an LA fashion editor and has since written for many platforms, including The Stars Scroll and tarot.com. Simone's book, and I want to hold this up because this is the one I'm almost finished reading, which is Astro Feng Shui, making magic in your home and life, as well as moon power, lunar rituals for connecting with your inner goddess. Bring ancient secrets into modern living. You can read Simone's blogs and learn about her weekly Patreon show. Simone says at astroalchemy.com. Simone, welcome to Dear to Dream. It's great to have you. Thank you. I'm very excited to be here. That is so cool. I'm going to bounce, I guess, a little bit because I know we're going to talk about where to live. But I just want to start with this, reading this book. And because you and I have done a little bit of work in the past, I'm so fascinated by the ideas here. And I'm already seeing a couple of things. I was like, Oh, my back is to the door. I never actually thought about that.  And I'm amazed I didn't think about that my desk is set to the wall. This is my workspace and my back is to a door. Will you talk about that real briefly right up front? That is a very important thing to work with. I mean, some people's offices are set up in such a way. Mine is actually a good example of that where there's no other place that I can put the desk than when where my chair faces the door. And one day my cat came in and sort of attacked me out of the blue, which is really kind of the reason that this problem, this is a problem, right, is somebody can come from behind theoretically, or even your pet and starting you. So it's like, you've got to have a strong back. And there are cures for that. You can put you can hang things up like something red, a red tapestry or red is a really strengthening color.  But the very first line of defense is to try to do just the opposite where you are facing the door so that when people come in, you are, you know, in the power seat. Tell us. So you say red. So what do you mean?  What if we can't even hang a red tapestry? What else? What other triage can we create? Oh, you could you could hang a red sweater on the back of your chair. There's any number of clever creative ways you could get some red at your back. You know, and the idea being or you could wear something red, of course, or you could paint your chair red for that matter. Or I don't know, I mean, is is what we're looking at here in this photo in today is this your office. So we're talking about this screen behind you? Well, yes, you know, I use the screen for my podcast or when I teach my classes purposely to disconnect visually for the viewer, the rest, and to have a really lovely background. I mean, actually what's behind it is nice too, but I don't need people to see the mobile and the lamp and the this and that I like to keep it, you know, more present. And this is my white chair, which is funny.  Yeah, well, hang a red tapestry or a red sweater on the back of that or get a red chair. Or you could, if you really wanted to invest in something new, you could get a different screen that has red in it. Yeah, that's way possible. Interesting. Okay, love it.  The other thing, so I thought about a friend who has a stove that has a little bit of a leak, they've had the gas company out, they can't figure out, I don't know if they need a new stove or whatever. It's very faint. But once in a while, when I walk in their house, I could smell the leak. And I read in your book, stoves are about wealth. Yeah, talk about that. Absolutely. That's why they say always keep your burners clean and in working order as well as the oven itself. So if there's a leak there, then I would be willing to bet these people are having trouble holding on to money, or that it's just leaking out in some way. That you know, our environment is speaking to us at all times. That's what Feng Shui is about. That is so fascinating. So I believe very much in Feng Shui. And I know that once upon a time, way before I met you, because I would use you, but a long, long, long time ago, when I first heard about it, I was quite young and I had an apartment done. And I remember I wanted to fall in love and they had had me do these things with flowers and colors. And so you know, I felt honestly, I know in your book, you address that some people feel overwhelmed with the changes. I didn't feel that way at all. I felt really excited about implementing a crystal here, just these little touches. But I will say I had someone come in my life very quickly after that with great ease. So I believe in this. Yeah, yeah.  Just like me, we love our homes. We love fixing them up and changing them and being as cozy and comfortable in them as possible. God, is that the truth? It is the nest, the haven, cannot be cluttered, cannot be chaotic. It has to be like my fresh bed. Every my bed, I have to buy the, you know, I have to get an expensive awesome bed. I have to have like my bedroom be a sanctuary, all that stuff. Absolutely. Outside of my place, I will say, there are a lot of overgrown trees and bushes. I find it spectacular. In fact, it's one of the things that captivated me when I came two years ago to see this place. The manager felt I might be turned away, looking outside the patio or the bedroom window and seeing all this greenery and not instead the street or something.  I feel like I'm living in a jungle tree. It's awesome. So there's not a ton of sunlight that gets in here. Is that a plus? Is that an impediment to have that much growth going on? I mean, my spirit loves it, but I don't know Feng Shui wise if that's a cool thing. You know, who cares about Feng Shui? If your spirit loves it. If it were blocking out all the light and your house, your apartment was dark and dingy, and you didn't feel a sense of growth and lightness within it, then it would be a problem. But you know, Feng Shui is very practical.  If something is off in your environment, it's just obvious. So it sounds like it's just fine for you. And I think having greenery surrounding a place is a plus. Yeah, that's cool. That makes sense. I can imagine some people walking in here and seeing that and being like, no, they'd want it all cut down and see the street. And for me, it's like, I love that I can live in Los Angeles and feel that I'm like in some forest somewhere. Yeah, that really works for me. And so I think I'm going to switch because there's so many questions I have for you. I love what you do out in the world. I love the service that you provide. And I think it's fascinating all of what you provide. And by the way, I researched you. And I was really impressed because you're on a lot of important sites, you've done a lot of work, like you have a big amount of beautiful work and connection with community out into the world. I know your books even have beautiful reviews from people. So kudos to you for really aligning with why you're here. And just tell people so before we get really full into the where to live in the world and how you help people and what we should look for. What are all the services that you offer? Well, first, I just wanted to say as we were talking about feng shui just now that the astro part of that is working with the new moons. And that's what my book is about. The new moon is the time every month when the sun and moon join. It's like a seed point for the month ahead. It's the power point. It's when the moon is dark in the heavens, but that doesn't make it any less powerful. So those are the times that you work with a particular part of your house. And for those unlike you and me who do get overwhelmed by the thought of feng shui their entire house all at once, this is a way of taking it in bite size chunks. You know, you're working with one room for that month. And so that's how that astrology part, which is very simple to understand the new moons, fits in with the feng shui part. So that's something that I, a system that I devised, gosh, about 10, 12 years ago now. And, but I've been studying astrology for many years. And so I offer the basic services that most astrologers offer relationship readings, transit readings, which is like, what the heck is going on in my life for the next, you know, year or so, it's usually about a year's forecast. And just so you know, it's not a psychic reading, some people mix up astrology with other things, or they don't quite understand what astrology is. And astrology is based on the map of the heavens at the moment that you were born. And it's really important to have an accurate time of birth, especially for what we're about to talk about next, which is the astral locality. Because if you don't have an accurate time within say five or 10 minutes, then that particular reading is not going to work for you. There are other readings that we can approximate without the time of birth. But in this reading, we got to have it. So address that for a second. As you know, my boyfriend has adopted. He doesn't know his time of birth. Right. What would you do for somebody like that who still wanted to work with you? Well, we cast what's called a solar chart. That means I'm casting it for 6 a.m. when the sun is on the horizon. That's what we do for a person because there's plenty of people that don't know their time of birth. And so it's better to have a solar chart than to be guessing. It's much worse to be guessing and have it be wrong, you know, wrong within hours. Right. And so if when you say a solar chart, you mean you can still semi predict, well, this would have been your ascendant and this would be your moon issue. Well, no, what it does is it gives you the same ascendant and as your sun sign. That's why we call it a solar chart. And it's accurate as far as it goes. It's just missing things. And sometimes people are born on the day the moon changes sign, the moon changes signs every two and a half days. So it is possible without knowing the time of birth that you may be guessing about the moon sign. But because the moon represents your emotional nature and your instincts and, you know, basically who you are on a more sensitive, hidden level, it's often, especially if you know someone, it's often pretty easy to figure out which moon sign is, you know, is right. It fits best for you. That's interesting. And the other things you were talking about, what you offer. Have you covered all of that? I want to make sure you get all of that to us. Just different types. I feel like I'm missing something. I can tell you one, which is colors. That's how I met you, by the way, you came off of stage and event. And all I knew is this woman, you were so adorable. And I wanted your outfit, although I don't think all the colors will look great on me, but I could have stolen that outfit. It was so awesome. The pants, the top, the sweater, but it was captivating to someone like me is very sensitive to that. And I love fashion. I love when people have the right clothes on. And so that's how I initially was even attracted to you. And I know in our reading, you suggested to me close to wear, which by the way, I've been following every day of the week. So today is Wednesday. You told me to wear green and wearing forest green. So that's something you offer as well. That's true.  And I wrote an ebook about that. So it's a way of aligning yourself with what the planetary ruler of each day is and what colors and energies pertain to it, such as, in fact, we met on a Wednesday when I happened to be wearing teal. And I'm wearing teal again. And I put my green background behind me because teal, green, turquoise, these are all colors that relate to Mercury. And Wednesday is Mercury's day. So we want to honor Mercury, the God of communication on the day that he rules. This is very ancient astrology. This goes back to the Babylonians, which is where astrology began many thousands of years ago in Babylon and Mesopotamia and that part of the world. And it's been lost. Most people have never heard of this. They have no idea that Monday is the moon's day. And yet we talk about, you know, blue Monday or that Monday is a day where people feel very sensitive and very, you know, more in touch with emotions.  And then you take it to that level of, oh, what's my ruling planet? And therefore, what is my day? And this is then becomes my power day. And you can, you know, work with it on that level as well to consciously dress in the colors and the gems and the fabrics and everything of that planet. That's great. I love that because I teach visibility out into the world. And as I'm listening to you, I'm realizing that's an aspect I never considered for my clients before is how important it is. So now they've got all these tools, they've got, had all this inner healing work around visibility. They also have the strategy and the full on pro technique how to get out there. Ta-da! The next piece is how you're presenting yourself in the fabrics and the gems and the, you know, or if it's guys, whatever beads right now that's really big for guys to wear. But the clothing and the style and it's like, I love this. It's so complimentary. Yeah, yeah. Well, I love art and design and beauty. And as you said, I'm a former fashion editor and I often offer events here at my house in San Diego where people come and we do rituals, we talk about astrology, look at people's charts, and then we make collages because I'm really big on vision boards. I do them in a slightly different way than most people know about. And it becomes part of a very deep process of identifying, getting in touch with what your subconscious self really wants and then creating a visual image that speaks to that. Oh boy, that's so amazing. Okay. Well, so I'm big on that. So I'll stay in touch with you about that because I've got one still hanging that I created a year and a half ago easily. I still love to look at my vision board. It's still, there's something, there's an energy attached to it that when I look at it and the reminders and the words and the visuals, it's like, oh yes, I am creating that. And a lot of that's been created and here I'm still headed. So it's an exciting, exciting way to create an energy I think out in the world. And so speaking of world, let's talk about astralocality or astro-cartography. For anybody who's not heard of that, will you briefly explain what does that mean? Why would anyone do that? Well, it's a way of taking your natal chart, which is the map of the heavens on the day you were born and relocating it to different places throughout the world as if you were born in those places. So there are some areas of the world that are more intense in either good, bad or indifferent, you know, but just more intense for you than others. And there are some that are just sort of neutral. So astralocality will show you the different lines. And when I first talk with people before I do the reading for them, I ask them to fill out a form telling me, first of all, what kind of climate and terrain are you interested in? Because I don't care if you got the best line in the world, if it's going through, you know, Upper Siberia or whatever. And you don't want to live there, obviously. Or like in, I hope you don't mind my sharing this point, but one of the places that came up as favorable for you was Berlin, Germany, right? Now, you happen to have a good line through there. And yet, for whatever reasons, and you can talk about that if you want or not, but it's not a place that you would consider living, right? And yet, there are ways that you can emphasize different areas of your life through astralocality. Let's say you're looking for love. Well, you might want to go to a Venus line. Venus is love. And that shows where your natal Venus, the Venus that where Venus was when you were born, where that's most prominent throughout the world. And there's different. There's a Venus Midhaven, which is Venus to your career point, bringing Venus and Jupiter are what's called the two great benefits. And benefit means positive. And favorable. And so unless this is where it gets really complicated. Some people have, you know, a Venus or Jupiter in their natal chart that's not very well configured, in which case, those might not be the best lines for them. But in general, Venus and Jupiter lines are the ones you want to be on. And also sun lines. Like for you, you have a sun line, your sun in cancer is running right through LA where you live. This is why you feel so much in your element there. It's because the sun is your life purpose. It's your radiance. And this is one of the most quote unquote visible lines that a person can live on. So here you are. You gravitated to it and you have now found your niche there. That is, thank you so much. That is so interesting to me because I will say growing up in New York, which you said was also a strong point for me, but I have new plans to go back and live there because you said it right up front. Climate. Done with winters. We'll never do a winter again. I grew up at a young age through my young teenage ages dreaming of moving to LA and I had never set foot here. That's all I knew. I was so powerfully drawn to move out of New York and come here, sight unseen. Wow. So my first experience stepping off a plane was checking out colleges, choosing USC and they chose me going to performing arts and suddenly boom here I was and it's like I may buy a home other places. I may move to Northern California sometime and also have a house there because I love it as well. But I really love it here for many, many reasons. So that is so cool that even at a time I didn't fully understand what intuition was or gut responses. I was still responding positively. Well, the sun is an especially important planet for you because you have Leo rising in your chart and the sun happens to rule Leo. So not only is it, you know, the sun is always an important planet for everybody, but it's doubly so for you because it's it's what the ancient astrologers would call the captain of your ship. It's a kind of archaic term for the planet that rules the Ascendant and it's your power planet. So in order to really be in your power, living on a sun line is crucial. And as when we talked before, I mentioned that the same line runs up through the Bay Area and you said that you weren't interested in living in San Francisco, but now you're saying Northern California, which is also that same line. So it's, you know, obviously it's going to be somewhat different. There are mitigating factors up there that you don't have down here in vice versa, but it's the same line. So it's also a great place for you to be. I love it. Yes, exact exactly. It doesn't have to be San Francisco. I'm not drawn there, but I can tell you, I don't even want to tell people the city because I feel like if I tell people the city I love up there in Northern California, everyone will move. I will say I got an Airbnb once after a workshop at a city, a town I'd never heard of before and I was blown away. I was like, Oh, this is so heaven. It's a city. It's close enough to San Francisco, but not in San Francisco. It's surrounded by forest and lakes and water. It's upscale. Forgive me, Lord Jesus. I love beauty and luxury. It was a very sophisticated town, sophisticated restaurants, had a lot of health food stores. I was like, I have landed in Eden and it's the first time I'd considered that before. Oh, and the weather was good. It was unlike San Francisco. That's very cloudy. It was quite sunny and summery. So for all those reasons, yes, I definitely feel that there's a place at least one. I'm sure there's more that I fall in love with. So we're going to just take a quick break, but I hope you're starting to realize a little bit some of the possibilities. When we come back, we're going to get deeper in this and Simone's going to show us how what a map looks like. What is your cartography even potentially look like and all the lines and it's pretty cool. I can't wait to see it as well. So this is the Dare to Dream podcast and I'm so grateful that you're tuning in and listening. And as my gift to you, I offer three months free of the Thinkific business platform that allows you to create market sell and deliver your own online courses. You can get the tools super easy and turn your expertise into a money making career. Go to thnk.cc-deb for your free subscription. That's thnk.cc-deb. And if you're tuning in after we've started, this is Debbie Daschinger and Dare to Dream. I'm interviewing Simone Butler. She is an expert astrological guide with more than 30 years of experience. You want to go to astroalchemy.com. So I want to just sum this up before we get started and looking a little bit at maps from what I think I understand in everything that I've been reading, that astro locality is actually a modality that someone like you in astrology uses. It shows how moving to another country or location is like moving to another part of our birth chart. Yes, birth chart can be spread across the planet starting from our exact time and place of birth. And this shows just where all of our planets, our signs, our houses are going to lay out geographically. And the place of our birth is in our ascendant house or first house. And to the left and right of it, or depending on how you're watching me, left and right of it are all the other signs and houses. So for example, if, let's see if I get this right, if Texas is in my Leo ascendant birth chart, California will be in the cancer part of my chart? I wouldn't go too far down that road, Debbie. That's, I don't think you're, and I wouldn't expect you to because it's a complex thing, but that's not exactly how it works. But when you see the chart itself, when I put it up, I will explain to you more how, how it works. But I do want to give credit to Jim Lewis who actually developed astro cartography or astro locality. I forget, I guess cartography is what he named it. And this was only just in like the early nineties that he developed this system. He's deceased now, but he is the grandfather of this system. So prior to that time, it's not like this is something ancient that comes from the Babylonians, right? This is a modern way of interpreting the chart. And it really does work. It's kind of amazing when you go to these different places and lines, you know, like I have a Pluto line through Arizona and I lived in Sedona for about two years. And it turned me inside out. That's Pluto. It was very intense. It was like, I love the land there. I had such incredible healings there, but it was very hard to live in that place. And so it kind of has a reputation for chewing people up and spitting them out, even if they're not on a Pluto line there, but I was. So I didn't last long there. Okay, cool. So let's deep dive. I'm ready. Show us, show us the way to where we ought to be living. And what does this look like? Oh, keto. Let's view solar maps. And here we are. Okay, we're starting here with Europe. That's the first map that happens to be up for you. And let's look right here at this. Can you see where I'm indicating this line? Do I see where you're indicating them? I'm moving my cursor along this line that says Jupiter Ascendant and it goes up through Florence and Verona. Oh my God, I'm so happy. Can you see? I can't see it, but you can just keep speaking because people will be listening to the podcast as well. So just describe for those who can't see. But I can't tell you, you starting out in Italy, like without a doubt. I'm so drawn to that country. I'm ready to like, where do I buy a house? I love it there. Well, and that's because you have a Jupiter Ascendant line there, which is one of the most favorable lines to have. Now Jupiter does rule travel first and foremost. So I think it's important that you would go there and travel as much as possible near and along that line and really determine whether you, it's a line that you want to live on. I think you would do really well there. You would learn a lot. Jupiter is all about expansion and growth and learning. And some people do well living on a Jupiter line, but at the very least, it's just a very great place for you to travel to. And so as you can maybe can or can't see on this map, it goes straight through Florence and Verona. So those are the two places I would start with, although the way this astral locality works is the entire country of Italy is really colored by this line. You're still going to have favorable Jupiter energies in Rome, in Milan, Genoa and other parts of Italy as well. So it's definitely a lucky place for you, regardless of whether you end up living there or owning land there.  Awesome. That's the greatest news ever, really. Now just while we have this map up, the only other lines that you have through Europe go down from through France. It will actually start up in London. It's a Mercury mid-heaven line and it travels down into down Spain and France and Spain. So Mercury mid-heaven is also a travel line. Mercury and Jupiter are both lines of exploration. Have you been to London? I have. And how did you find it? How do I find it? Well, amazing. I don't want to live there. I can tell you right now, I don't feel a call to live there. It's nothing like what I feel in Italy. I, of course, loved it. And I mean history and a million amazing things. Yeah, I enjoy it very much. Well, a Mercury line is very stimulating. It's very mental. It's like, oh my gosh, there's so much to see and do, but it's not necessarily a relaxing line in the sense of, like, and plus of course the weather is such that you probably wouldn't want to live there for that reason alone, right? That's correct, yes. And yeah, if there was something you wanted to study or learn about, boy, that's the place. Now here's another thing to know about this system that's fascinating is the city and also it applies to people born there. Like people that are born in or near London or from England could play a role in your life through bringing you startling new concepts and information and that sort of thing. So that's another way that this type, this system works. You don't have to physically go to this line. You can meet people from this line or the general vicinity of it who can really teach you something important. Fascinating. I love that. That's like the red piece in the back of my chair. I don't got to change anything. I could just do a little bit of triage and it all works. I don't even have to go to London. I can have someone from London come to me, disseminate information and boom, life change. Yeah. Now there's another line here and it's Mars descendant. Descendant is the point of partnership and other people and Mars is considered to be one of the malefic planets. It's a little bit trickier of an energy. So a Mars line is something you have to examine very carefully to make sure that you're not going to be going to a part of the world where they're strife or where you're going to get into trouble in some way. So especially when it falls on the point of other people, you can fuss and fight with people on a Mars line. So if I don't know if people can see this, but where Mars and Mercury cross, which is southern France, is when the lines cross, then you really got a little vortex of power for good or ill. And Mercury's communication, Mars is action energy and sometimes fighting. So that would be an area to be especially careful of.  Well, you might, it might be very stimulating, but you might also fall into arguments there, which could be, you know, interesting on a temporary basis, or you might find that people there, the way they think or, you know, the way they communicate like I know in southern France, people don't speak English as much as they do say in the big cities like Paris. It could be a language problem that you run into that frustrates the heck out of you because you don't speak French, right? I do not. Right. So that would be if I were looking at the whole world for somebody and pinpointing places where there could be trouble for one reason or another, or where they probably would have want to avoid living in that place or spending a lot of time there, that would probably be one that I would choose for you is southern France. Very interesting. And especially because I'm a certified wine specialist. So one of the things besides travel that's so big for me is also the idea of traveling to some destinations for wine. Obviously Italy would be amazing. Spain would be amazing. I'm a specialist in those countries, France. And so to hear you say specifically southern France, I mean, I will pay attention to that. Yeah. I would be very curious to hear, you know, what happens if and when you go there?  It's more just things could be frustrating there for you. And so I would be curious to hear how that's going to play out. If indeed you go there. Okay, well, very good. It's really noteworthy because I don't know about you guys listening, but I will say for me, you know, the juxtaposition of where everything lines up, that might now not now be on the top of the bucket list. You know, if the why bother if there's going to be issues, there's so many beautiful places in the planet before that to go see. I want to talk a little bit with astral locations because it can determine things. And you tell me, Simone, vacation destinations, wedding destinations, places to relocate, because they each have their own unique characteristics. Talk a little bit about that. Well, when you said that, I just remembered what happened some years ago. A client of mine had her had me do her astral locality, and she was very curious about Ireland. She has heritage from Ireland, you know, and it's a Neptune line for her. And this was many years ago. And, you know, as astrologers, we learn and grow. And sometimes, you know, like at the time, I said to her, well, just be really careful when you go there, because Neptune is known to be kind of hazy, daisy, you know, you aren't seeing clearly, you're not making really intelligent decisions, etc. You can fall into addictive patterns. This is the downside of Neptune. Well, she went there and had the most amazing spiritual experience of her life. And she, so that's the upside of Neptune, you see, Neptune can bring you in touch with the magic of the land or the spirits, the fairy sprites or whatever it is. And the ancestral energies of that place is, that was the primary, you know, thing she experienced. Now, what it would have been like if she moved there is who knows. But the truth is that in traveling there, she had this profound spiritual experience, so that this is where it's very hard to know which way is it going to go. So I try, I try to present both possibilities. But, you know, there's fate, there's free will, there's a lot of things that astrologers can't know. We're giving you our best educated guess as to how these energies are going to be for you, but nobody knows for sure. Okay. You know, that's pretty big how things can go one way or the other. And so when somebody comes to you, I know there was a couple other places you had mentioned for me besides, you know, Italy, which thrills me to no end. Also Western Portugal, a place I've never been, a language, Mamma Mia, but still fascinated to go there. Western Ireland, Berlin, Germany, still fascinating to me. Although I understand from having armchair traveled there that because it's got a huge culture, very free spirited late night parties, lots of art, lots of expression, great food. Like I actually also understand, I mean, that I see the potential of how I might enjoy there. I still don't see myself living there, but I would love to go explore Stockholm, Sweden. That's really interesting. And the southern tip of New Zealand for me near, boy, what a name, Inver Cargill. Right. No clue where that is. Yeah, me neither. Well, it was the only city labeled on the map, which was anywhere near there. So that's why I mentioned it to you. But you know, in, in looking, you just mentioned Portugal and Ireland. And I, so I put up the map for that area. And it's a sun mid heaven line. Now, this is a very visible line for you. And because you're the visibility queen, that's one reason, and we already have seen that the sun, you're on a sun line where you are now in LA. And so here we have another high visibility sun line going down through the very western part of Ireland and Portugal. So what does that mean? Well, maybe you get your, your books do really well there, or you go on tours there and people love you. I mean, there's just so many ways that this could manifest. You don't again have to physically go there. Maybe you have connections with people from these parts of the world who end up promoting you and getting your workout to the world or advising you on your career mid heaven is the place of career in the chart. So it would be worth visiting those places. If you're wanting to just explore the world and see, you know, Portugal is quite the haven for Americans these days. It's one of the top place for expatriates. What a time to be saying that just a year before an election. So I may see all there. That's amazing. And other parts of Africa, because I did also ask about Africa, I would love to go there. And you said specifically southern Morocco, Mauritania, Guinea, Tunisia, Nigeria, wow, wow, wow. So astralocality. So for people who are interested, and I think we can take this down now and thank you so much for this. Oh, okay. You don't want to want me to look at Africa? I think in the last minutes we have together, I want to ask some other questions for, but thank you, my love. Everybody are really yummy idea of what's possible for people who are interested in this and this astralocation for themselves. I want to just address some other ideas of how this can be used, because I really find this fascinating what people can come to you for, like for business, for attracting clients, or for pursuing education, or I want to improve relationships, I want to travel as you mentioned, or I want to expand my creativity. Talk about the ways people can use astralocality. Oh, yeah, you can combine it too with the transit reading, because let's say that you're looking to expand your business in a new direction, and you want to make contacts in different countries, you can figure out not only the timing for when is best to be doing that, but the countries that are potentially going to be most receptive to what you have to offer. So you can use astralocality for business in that way, you can use it for relocation. If you just want to travel and have a fantastic or a spiritual experience where you're traveling to, there's any number of ways you can use this. Simone, forgive me, because I'm getting a massive download for you. I really hope you have a package called Astro Mastery. I'm for real, I do this with clients all the time, but I hope you have an Astro Mastery, because I'm listening to you, and what I'm thinking about is the package that I think would be the most appealing, and again, I don't know your services, is the fact that you can do the Feng Shui of the house, which I know is tremendous what that can create in getting everything in order, and then you, it's sort of like within the home, as well as from outside the home.  And then when they're ready to go out in the world, where should I be living for my career, my money, my health, my relationships, my love, everything that I want to be doing, and my greatest joy and happiness. That seems like it's not a trifecta, it's a double ecta or something, but it seems incredibly powerful of an offering to people. Is that something that people have come to you for just because I'm on fire right now? Well, I do not have a package called Astro Mastery, although I love it. You're so great with coming up with, in fact, the whole idea of a hot spots reading, what we're offering as a special to your listeners, that was your term, hot spots, right? I love it.  Also, you know, your son is conjunct my mercury to the exact degree, which is why we've connected so strongly. And so you have an ability to do that for me. I don't know if you do, I would imagine you do that for others too, but you really have zeroed right in on what I have to offer. So I'm so grateful for that.  Yes, I do this for clients in private sessions all the time. I mean, I teach classes, but we do private sessions and thank you, you know, universe for downloads, but I am so excited about what you do. I really am. And I want you to talk about thank you for bringing up the hot spots, because I will share and give you gifts and tell you to go do things and then I forget. So tell us what about the hot spots? What are you offering people today? How can they work with you? What are they going to get? Right. Well, what we will do is I've given you a link to offer that special to your listeners. It takes them to a hidden page on my website in which only you will get this special deal. The hotspots reading, which is normally 150 is only 125 for your listeners. And what it involves is first you'll fill out a very short little questionnaire that says what kind of climate and terrain you're interested in or what area of your life you're wanting to emphasize. Like, is it health? Is it family? Is it love? Is it there can be more than one, but we need to know what you're really looking for and what you really don't want. If you got to be by water, I need to know that, you know. So then after I get all of that, we'll, we'll chat on the phone. We'll look at some maps and narrow it down the three locations for which I will produce a special report for you that breaks it down those three locations. And I sent you some of those. So you know what that is. It's a report, people. It's not going to be like two bullet points. You're really going to get fully fleshed out. Why that location and what in that location and more. And just so you know, sometimes there are downsides. Sometimes it's not just totally free and clear. This is it. Go for it. Sometimes it's like, well, here's this influence, which is also a little bit of a caution. So just to be aware that, you know, that may show up for you as well. But I'm going to do my best to find you the absolute best places throughout the world or just this country that for your particular needs. So that's what that special. That's huge. I love that. And I love that they get to fill out a form too. So yeah, for some of us, obviously, terrain is important or maybe you want to stay close to your family or something or job or something's up. But, you know, there's, there's so much more. I mean, there's so many elements that go on in somebody's home. So the hotspots tell us where do we go? What is the URL for that? Well, that is the link that I gave you. So you'll have to put that somewhere that people can find it. Let's see if I can find my dear Simone, so I can say this on the podcast out loud right now. But I believe, excuse me, excuse me, that this is, let me see if I can pull this up. And you can look too. But I really want to say it out loud so they have it while we are, because I think it's the, and I want them to get this special. Thank you for being patient. Here it is. Yay. It is. It is. H-T-T-P colon slash slash astro alchemy, that's A-L-C-H-E-M-Y dot com slash hotspots. Okay, cool. So it is basically what I had read earlier, slash hotspots. So if you want this special for Dare to Dream only, man, do it, do it, do it.  What a deal. And again, that's astro alchemy dot com slash hot spots. So you could be hot in your spot right now. This is Dare to Dream. We're at the very end, my dear. Thank you so much for all you brought. And what are you next, Dare to Dream, Simone? What are your future dreams and goals? Oh my goodness. I'm looking for my next place to move to. And of course I have some in mind. And I'm intending to visit them. And my dream is an eco village to live in a village atmosphere on the land and be connected to artistic, wonderful people, like-minded folks, and have a sense of family, but with my own private space. So if you looked into Fairfield, Ohio. No. It is a community. It's actual city in a community. And they do TM. And their entire culture is predicated on community meditating. They've got, I mean, from children on up school systems, the entire thing, some very prevalent transformational names that you know, live there. I don't know that popped in when you said looking for a place like that. But check out your lines. Let me know if there's any congruence there. I don't know about that, but I definitely want to live in an earthen home. I have studied earthen building for a long time. And as a cancer, there is nothing more wonderful than being inside warm, curved, earthy walls. I love it. Yeah. I feel your girlfriend. Well, thank you, Simone, for coming on and sharing your brilliance today on Dare to Dream. It's really been a pleasure. Oh, definitely. Thanks so much for having me. I end today's show with this quote from Lee Goldberg. Astrology is like a weather report. It tells you what conditions you're likely to face in the future. If the weatherman says it's probably going to rain, you're bringing umbrella. If you follow that advice, you won't get wet. Again, the special that Simone is offering, if you'd like to know where in the world should you be living, is astroalchemy.com slash hotspots. In next week's Dare to Dream, I'm featuring Brandi Alessandra. She's one of the owners of the only medically licensed luxury plant medicine resort in Costa Rica called Rhythmia. Tune into this enlightening transformation conversation each week on Dare to Dream. Remember to subscribe. You can also get the YouTube videos at youtube.com slash deb on the radio. And remember, the secret of success is having the courage in the first place.


Today, I thought I'd share my weekend morning routine and a little get ready with me too So my weekend breakfast is a little different from during the week I never have juice during the week and I certainly never have pancakes But I try to bribe myself with having as much fruit as I can on the weekend by having some pancakes with them After breakfast, I like to do some meditation And if it's a beautiful day, I'll meditate outside Or if I can't I'll light some candles and meditate inside And I want to shout out today's sponsor, which is Jewel Candle These aren't just ordinary candles inside each one, it's a piece of jewelry So if you're looking for a gift for yourself or maybe even for Mother's Day You can head over to the website, click the scent that you like Pick the type of jeweler you want to be in it And they also gave me a discount code, which is the Makeup Chair 20, which you can use at the checkout They've been one of my favorite candle brands for such a long time And I'm so grateful for them for sponsoring this video Typically on weekends, I don't wear a lot of makeup, but I was heading out with my sister after this So I thought that I would do a little get ready with me So I start with some miracle treatment This stuff smells amazing And I just pop this through the ends of my hair I then use the babelist curler And if you haven't tried this, you need to, it's like magic It's one of my favorite ways to curl my hair, particularly if you have chronic fatigue like I do And then I just add some texture with some salt spray For the face, I start off with a little bit of color corrector And then I use the L'Oreal True Match Powder My skin's a little dry at the moment, but it still worked For the eyes, I keep it really natural I start off with a brown tone, working this through the crease and onto the lid And then with a really pale shade, I pop this over the top of the lid And then a little bit under the brows too Next, I curl my lashes and add some mascara And for the face, I'm actually going to be using a finishing powder This is in the shade Dark And this brush does all the work for you I like this because it's really sheer, but it also adds a beautiful tone This just adds a little bit of depth while adding a little bit of shape to the face One of my favorite blushes at the moment is this beautiful Floormar blush I popped that on using the F41 I loved it so much, I actually put it onto my lid as well So take a large blending brush and just pop this on the outer corner and through the crease It's a great way to bring the whole look together For the lips, I lined with a lip liner And then I use this beautiful lipstick This is by YSL and it is so gorgeous I was just showing my sister and even she agrees It's yummy And then just to keep everything in place, I finished off with a setting spray For my outfit, I kept it really simple Just a knitted jumper, a pair of skinny jeans I love these because they have a slightly brown trim So what I do is I match the brown trim to my heels And excuse to wear these heels, I will take it They're really really comfortable, I love wearing them I just paired that with a Tand blazer But I did pop the collar up a little bit Just to add more of a jacket feel, so it doesn't feel so structured And then it started to rain And the next day this happened But it did look absolutely beautiful Let me know what you guys get up to on the weekend I would love to hear from you guys And I'll see you guys in the next one


The study examined the role of secretase in Alzheimer's disease. It found that the absence of all three AF1 subunits in the pyramidal neurons of the postnatal forebrain leads to progressive cortical atrophy, neuronal loss, and gliosis. Additionally, it showed that the accumulation of membrane-bound fragments of APP, APLP1, NRG1, and DCC is increased in these mice compared to wild-type controls. However, the removal of APP did not prevent the neurodegenerative effects of the mutant mice. Instead, the researchers suggest that selective AF1 gamma secretase inhibitors could be used to treat Alzheimer's disease.


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Hey, my name is Alex from AlexFergus.com and today we're going to unbox the Juve Max red light panel. So I've been using these panels for a while, as you can see I've got the original here up on the wall. So this has just arrived. I'm going to take you through the unboxing and see what's inside, see what it comes with. We're going to do a quick little overview, see how big it is, how heavy it is, how to set it up. We're going to set it up on the wall, we'll turn it on obviously. And we'll do a really quick comparison between the original. I don't want to go too detailed with the comparison today because I will be doing a separate video where I look at the Juve Max, the Juve Original and the Juve Mini and we're going to do a full overview of cost, deans, size, all that sort of stuff. So today's going to be more about practical applications, set up, what's included, yeah. So before I continue, if you don't know what red light is, head over to AlexFergus.com and check out the links below because I've got a few articles on red light therapy and how beneficial it is. I've also got reviews of the red light original and the red light mini. So all of that will be on my YouTube channel and if the comparison video is not yet up, be sure to hit subscribe because that will be coming up in the next few days. Real quick as well, Juve Max is the biggest one of the Juve range. It's around two and a half thousand US depending on what version you get. So they do a combo one which is 660 nanometer and 850, that's what I've got here. They also do 100% near infrared which is 850 or 100% 660. So I've gone with the mid range one. They are expensive, the big one, I mean it's a big chunk of money but once you see how big it is, especially in comparison to the original, you'll see that like it's kind of worth it because you get so much more service air exposure. By the way, if you use code LX, A-L-E-X when ordering a Juve light, you will save a few dollars. You know what, enough of that, let's unpack this. It's going to be interesting because it is a really big box, like it's a huge box. So let's hope I can do it all on my own. As you can see, two 16 panels, did I count that right? 36, yep. So 16 panels and now when we compare that to the Mini down the bottom two and the original just five, you can see how much surface area there is. Let's take a quick look at it. So it's pretty thick, it's about two inches thick here. This is middle so it's solid. It's not like some of those grow lights you see on eBay that are just plastic. There are fans on the back so there's a fan for each panel.  When we look at the bottom, I think this is, well maybe it's the top, this must be the top. We have the power switch and then these little connections here which we'll use to hang it up. And then down the bottom, we have the power plugs and some feet so you could rest it on the floor because it's big enough. It is rather, sorry, it is rather heavy, bulky, so I mean I can handle it by myself but if you're putting this up on a wall you may need two people. So it also comes with a few cables, booklets. So let's quickly run through this. We have the instruction booklet, I had one already open so pretty much this has got a bunch of benefits, reviews, how to set it up, frequently asked questions, how to use it and technical specs. So you've also got these door adapters so the idea is these just wedge over the top of the door or hang on the top of the door and then you can hang the light from this hook here. Unfortunately this isn't wide enough to fit any of the doors of my current house so I can't actually do that. So they're no good at the moment which is a shame we are moving so maybe in the new place we'll be able to use it. Alright and then I came with all these cables. Now the idea behind these cables is so you can hang it up on the wall. So if you look over my shoulder here I've got the original hanging, these bolts and then this pulley system hanging from the wall. So you can do that with this one which is what I'm going to do right now. So I actually had to refer to the manual here because in the package with the original and the mini it comes with this pulley adapter which is what I have up there. So if you've seen the videos for those unboxings and sit up you'll see me lowering it and raising it with these adapters. So I was wondering okay well there is no adapter for the max. And then I looked at the instructions and it states here, choose a set of support cables for the desired height of your device. So what I realized then is there's a bunch of different cables in here of different lengths. So instead of using the pulley system you just use a pre-determined length. So to make it easy I think I'm just going to go with one of the shorter ones. So let's go do that now. Alright so you can see the different lengths there for hanging it up. So that's instead of the pulley system. So I'm going to figure out which cable I need and then get them installed. So installation is actually rather easy. You just take these hooks, these cables I mean, screw them on like so. The carabiner, clip them on like that and then if you're using this on the door you take the door hinge and that will simply click over like so. So you do that twice because there's four or two lots of cables there, a bit of a twist there. But I don't have the door frame instead I'm going to hang it on those hooks up there. So what I need to do now is take this and hang it up there. Now in the instruction book it says use a second person. Fortunately I'm home alone and there's no one around to help me. It is quite a heavy device but I figured I'm big and strong and I lift weights for fun. I should be able to figure it out. If not you're going to see an epic fail on camera. So let's go do this now. Actually real quick you don't even need to hang this. It does have the stoppers on the bottom so you could simply sit it against the wall and have it on the floor. If you didn't want to just sit on the floor you want to lift it up a bit. You could put it on a box or a piece of wood and lift it up that way. You don't have to hang it. Of course if you want to hang it you can use the wall brackets, the back of the door brackets. And yeah you can hang it on the back of the door, back of the closet and your wardrobe or something like that. It's a handy place to have it. I'm putting it here in my living room office and I'm here for a few more weeks and then when I move I'll put it in the office for good. But yeah you're not sort of limited to where you put it especially with those door brackets as long as they fit on your door because unfortunately they don't fit on my door. You know let's see if this is going to work and I realize I need to put longer things on. Alright I've hung it up there but as you can see my measurements aren't really right. Not even close to. In fact those brackets were already there so I just hung them on there. But I'm not going to do that because I think there's going to be too much strain coming through those two points. So what I'm going to do is take that down and because I'm in here for a few more weeks I'm just going to sit it on a box to get it at the right height and when it gets to my new place I'll measure it all up and put it in properly. So I'm going to take that down now and then sit on the box. Alright so I've got it there, sitting on a box, it's going to go all the way back so I can get it all on screen. So it's just sitting on the box it's not hanging from the top now which is actually a pretty good height because if you see me standing here next to it it's pretty much in line with my head and I'm getting full coverage from the knee up. Let's see if we can get this on a better angle for foxes everywhere now. Yeah so you can see it's pretty much head height and just below the knees and yeah I do have the original just hanging next to me and so I can get raised on the side and then yeah I've got a little mini down there which I actually want to put over my head so it's coming down on me but that's a sit-up alright so sorry it was so long getting all that sit up but you can see the size difference here between the max and the original so the idea is using this I just use it on my back and that's been around use it on my front and I'm getting my full full body whereas with this original it only really does half so you got to do one half and then the other however it's really good for the side because it's probably the right width so anyway that was rather long sit up but hopefully that shows you what's included with the Juve Max and then how to set it up and how not to set it up and yeah at practical applications you know again you can put it on the back your back it on your back it of your bedroom door you can put it on a closet hanging in your office you can hang in your bedroom or a bedroom wherever just um probably if you're gonna put it straight on the wall probably measure out the brackets a little excuse me a little bit of the night it well even though one of them was already there and then you've got a variety of cables down there to use depending on how high or how low you want it it doesn't come with the pulley system like the original does there but to be honest once that things up you're not gonna want to move it like like you just saw it's doing I'm 5 foot 10 178 and it's doing top my head down to my knees and it's covering all of that and that's kind of perfect and then I can use the original lower to do the side or I can use the mini if I want to do you know download so anyway hopefully it gave you a bit of insight to be honest if you do get one of these I recommend unpacking it with the second person because it is quite bulky and large and heavy and even getting out of the box was difficult again I got the the max combo so we've got red and near infrared and the red light in there what I'll do is actually plug it in real quick it does come with a rather long cable also I didn't show this before it comes with a cable it's about the power cable about two meters two and a half meters long I don't know what that is in feet maybe 10 feet I'm in New Zealand so I had to get an adapter because it does come with the American plug also comes with this timer which is actually really useful so you just see your time let's say you want to determine it's on the front and then where you go and it will just count down at beats when it finishes really good but even better than that it's got a little man magnet on the bottom on the back so it actually sticks to the panel so really really handy you don't have to use your phone so I'm gonna plug that in real quick so you can see it working probably should have done this before I rested it on here so there we go putting out a lot of light if you're wondering why not all the lights are shining it's because the lights that appear like appear then be the lights that appear not to be working are the 850 nanometer light so it's your near infrared light so that's invisible to the naked eye which is why you can't see it when shining at the 660 nanometers so I don't know if you can hear the background where there is a bit of noise here but it's not you know it's not overpowering I mean you can still have a conversation you could still be watching TV or whatever it's just like this you know it's like a fan noise it is a little bit louder than this one of course because there are more fans but it's nothing crazy I don't really know what else to cover if you have any questions I'm just gonna turn this off if you have if you have any questions please leave them in the comment section below if you want to know how to use it or whatever I have written a few articles on red light so check them out as well I've reviewed the many and the original and I'm done unboxing videos on them so be sure to check them out I'm gonna do a full comparison between them all they should be up soon so if it's not up already be sure to subscribe and yeah by the way if you want to order one of these use code Alex ALEX and you'll save a little bit as well but again if there's something I've missed please leave me a leave me a comment or question below so yeah I know it wasn't probably the best video to show you sit up but I can't use these on the back of the door if I could you just lock you just sit this on the top of the door and then you don't drop it like that sit these on top of the door and then you use those or these cables which I have on the floor use these to clip on and that's it ties on to the top which would be perfect I especially using these shorter cables because then you pretty much got the right height sit on the back of the door it's not in the way of anything especially a bedroom door and yeah I mean you've got you've got a red light in your bedroom when you wake up you know or at night before you get a bit or whenever else you want to use it for me I actually want to sit it up like this when I get into my new place so I've got the max on the front and then the original on the side and then do you know 10 minutes on the front so get in front and one side spin around back in the other side the mini I'm not too sure where I'll use that yeah I'm thinking over here but I'll sort that out when it gets in your place anyway I'm gonna leave it there again if you've got questions let me know otherwise give me a thumbs up or thumbs down and we'll leave a comment or whatever else you want to do bye


ज़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़़� ॐॐॐ ॐॐ ॐॐॐ oOO ॐॐॐॐ ॐॐॐॐ ॐॐॐॐ ॐॐॐॐ And we also said that the whole purpose of doing statistics, the reason for following so much of science of statistics, is to understand the population through a random sample. We said that if the population distribution function is known to us in up to a level of its form, then we say that it is a case of parametric estimation, where we have to estimate the parameters of the distribution. But if the form of the distribution itself is not known then we call it a non parametric case. In the present course, we are going to consider only the parametric case. Then we introduced what is known as sample mean. को कुर्वाऄ ज्बूठने सू好 आठ organisations or distribution, so we assumed that the population distribution f has a mean mu and the standard deviations, सिघ्मा and then we introduced what is the quantity, a statistic called Sample Mean. वी बनक्यते nearer to the expected value and its variance, वी भी वालताते आभाँ, through central limit theorem. वह वह आश्वाँ, we basically say that its expected value is same as the population वह आश्वाँ, is the population variance divided by its size of sample. And the central limit theorem we said that as if n is very large, the population mean will tend to a normal distribution with mean as population mean I am sorry. ग़ात्ते हैं भी ब्रत्वार, मैंत की तिताना हैं, मैंत की Wagat koi दिए की यह ज़ू़ के रहाता है, एक विस्ग रहाता हैं, अगर भी विस्ग ग़ाता हैं, श़म चल। sempre the enter Charlotte दर थश्धind token श़म अक श्ध चल तर्ग और उर उरकन Israel वी और � always वी तो तर्ग तत नद身 ठ सब क़ाष्ट. और घैंगे खॉने गाश्ढते, इवरे ना दरमद Firebase वी धॶiovascularंने वी श़म॥ít Left Inval Variators of ëSum off independent normal variablesí and Soms off independent chi-square random variables, we will use these properties to derive the sampling distributions from a normal population and we will see that if the sample is drawn from the normal population what is the distribution of sample mean and तुब बज़े बनाच ज़ूँ कर तुभ तुफ शुलग करतेग सर्फ आप आप इस पर toplane aamak aamak karetele तुफ शुलग तुफ ज़ूँ करतेग सर्फ आप आप यो यो तु� valve8 तुफ ज़ूँ करतेख सर्फ आप यो आप करतेख। atiya karkahtyamak karetele। । first few lectures in descriptive statistics. अ। । । । । । । । is exactly the same definition. प्छ वन प्छत्ःय श्ब इस या जाए। । । X1, X2, X3, Xn take a common distribution । । । । । । । X2, X3, Xn be a independent random sample from a common distribution । । f with a mean value । । । । । । । and a variance sigma squared, then । the sample variance is defined as shown here. त । । । । it is a square is equal to 1 over n minus 1, multiplied by summation of xi minus x bar, x bar is a sample mean, xi minus x bar whole square, this can be simplified in this simplification form and it can be written as n minus 1 capital S square is equal to summation xi square minus n times x bar whole square. Let us try to find its expected value. So, with this we get that n minus 1 times expected value of S square is equal to expected value of summation of xi square minus n times x bar whole square. So, you take the expectation of each of these component and we end up with n times expectation of x 1 square minus n times expectation of x bar square. Please understand why summation xi square expectation turns into n times expectation of x 1 square because x 1, x 2, x 3, x n all are distributed identically as f with a mean value mu and variance sigma square. So, they are identical. So, instead of taking summation of n 1 of them, I can as well take n times the expected value of x 1 any one or if this is x 1, I can even take x 2. So, x 1 is not important, but what it says is that the common expected value from the distribution f is being taken. Now, we apply the general rule of random variable that expected value of any random variable w square is variance of w plus expected value of w whole square and applying these to each one of these component of expected value of s square, we find this and it finally simplifies which you can verify very easily through simple algebra. It is expected value of s square that is the expected value of sample variance is the population variance. We will learn in future this is called an unbiased estimator of sample variance. When a statistic like s square its expected value is exactly the population variance and s square is the sample variance, then it is called the when expected value of s square is equal to the population variance, it is called unbiased estimator, s square is an unbiased estimator of sigma square, we will learn about it more in future. Now, let us recall few things which we have mentioned in the past and in case it has not been, it is the first time let us start it. Let x 1, x 2, x n be independent normal random variables with a mean mu 1, mu 2, mu 3, mu n and variance is sigma 1 square sigma 2 square sigma n square. One way I have to put a comma so that it is not mu 1, mu 2, it is mu 1, mu 2, mu n and variances are sigma 1 square sigma 2 square sigma n square etcetera. Then summation of these random variable is also distributed as normal with mean as summation of means and variances summation of sigma square. Please remember when the two random variables are they are independent then the sum of variance sum of the random variable variance of sum of the random variables is sum of the variances. So, this is what we have used here. Next we would like to see in the case where x 1, x 2, x 3, x n are independent chi square random variables with degrees of freedom k 1, k 2, k 3, k n then summation of the random variables x 1, x 2, x 3, x n is also chi square with degrees of freedom as a summation of degrees of freedom. This should be very obvious because the chi square with k degrees of freedom itself has been defined as a sum of squares of standard normal random variable. So, the it just the additive nature of the independent chi square random variable comes very naturally. Now, let us consider so far what we have been doing. We said that f is some distribution with mean mu and variance sigma square. Now, I am defining the form of f and I am saying that it is a normal distribution. So, I am saying that now I am taking sampling from the normal population. So, let x 1, x 2, x n be independent unnetical distributed normal random variables with mean mu and variance sigma square. Then what is the distribution of sample mean? Well, sum of independent normal variable is distributed as normal. Therefore, sample mean is also distributed as normal with mean and variance as this because remember here I think I am telling something very obvious. Expected value of A x is A times expected value of x. So, this gives you that expected value of x bar is mu and expected a variance of x bar is sigma square over n which we have already proved. And therefore, if the sum of the independent normal variable is distributed as normal therefore, sample mean is distributed this and further normalizing it the random variable x bar with respect to is mean and variance we get x bar minus mu divided by sigma square root n is distributed as normal 0 1. Please remember x bar minus mu divided by sigma square root n is called normalizing random variable x bar. It is also known as standardizing random variable x bar. So, for any random variable if you do any random variable w minus expected value of w divided by variance of w is the normalization refers to normalization. So, it says this is of course this is not just normalization it is actually a normal distribution. So, this defines the distribution of a sample mean when the population itself is a normal population then the sample mean is distributed normally as mean as a population mean and variance as a population variance divided by size of the sample and if you take x bar minus mu divided by sigma square root n it is distributed as normal 0 1. Now, if you take a distribution of sample variance we have to do some calculation in order to understand it. So, let us start. Sample variance is nothing but I mean we will start with x i minus mu whole square summation of x i minus mu whole square we have a so I can add and subtract mean sample mean from it and then this will be simplified to this value. Please remember here what it is using is summation of x i minus x bar is equal to 0 this is identity which is used here to get this term and therefore if you divide throughout by sigma or sigma square what you get is x i minus mu divided by sigma whole square is equal to summation of x i minus x bar divided by sigma whole square and then I am taking square n out if I take n out as the square root n comes out because I am taking a square value. So, this becomes square root n x bar minus mu divided by sigma whole square. So, I have basically divided this by sigma square and this by sigma square and I get this identity. You see this is very beautiful. Can you see that because x i is distributed as normally with mean mu and sigma square x i minus mu over sigma whole square is a chi square variate because this itself is a standard normal variate. Do you see this? This is distributed as normal 0 1. Agreed? This we have already shown that it is distributed as normal 0 1 and these each individual one are distributed as normal 0 1 and therefore we are taking summation and then you are squaring it sorry you are squaring it. So, the whole item will become a chi square and it is only one normal standard normal variate. So, it will be chi square with one degrees of freedom. While here you are summing up chi squares each individual if you look at this whole individual it is distributed as chi square as 1. They are all independent because x i's are independent and therefore the summation of n chi squares will give you chi squares with n degrees of freedom. Shall I explain it again? Let us start. From x i minus mu whole square summation i runs from 1 to n. I have not written it here, but I think it is obvious this is i is equal to 1 to n i is equal to 1 to n ok. So, then what first we do is we take difference x i minus mu whole square summation i is equal to 1 to n. I add and subtract sample mean x bar and then it simplifies to summation of x i minus x bar whole square plus n times this n comes because of the n summation because this does not depend on n. So, it is n times x bar minus mu whole square sample mean minus population mean whole square. Then I divide both the sides by sigma square and then what I get is summation i is equal to 1 to n x i minus mu divided by sigma whole square plus summation of x i minus x bar divided by sigma whole square plus I take the I want to take a square out. So, I take square root of n x bar minus mu divided by sigma whole square. Now, what am I saying is that this inner part x i minus mu over sigma because we have said that x i is distributed as a normal distribution it is coming from a normal population with mean mu and variance sigma square. We get a x i minus mu divided by sigma as a standard normal random variable. So, x i minus mu over sigma is distributed as normal 0 1. Similarly here we know that x bar is distributed as a normal random variable with mean mu and variance sigma square divided by n. Therefore, x bar minus mu divided by sigma divided by square root n is also distributed as normal 0 1. In other words, standard normal random variate. Now, we take a square of it. So, this is where we take a square of it. See if you take a square of a one single standard normal variate, then it is distributed as chi square. Here we take n of this standard normal variate and we take square of it and we sum it up. Now, remember each x i is independent. So, x i minus mu divided by sigma is also independent and therefore, x i minus mu divided by sigma whole square are independent for i is equal to 1, 2, 3, and therefore, you are summing up n independent chi square random variates and therefore, it becomes chi square with n degrees of freedom. The question is what is the distribution of this? Now, if we use the fact that sum of two independent chi square random variable with degrees of freedom n and m is a chi square random variable with a degree of freedom n plus m, if we use that very reasonably we can say that this should be distributed as chi square n minus 1. I repeat, we know that if the two independent chi square random variables are distributed with degrees of freedom respectively n and m, then the sum of the two random chi square random variables, independent chi square random variable will be a chi square random variable with degrees of freedom as sum of the degrees of freedom. So, it will be n plus m. So, if you consider that this is 1 degree of freedom chi square random variable which is added into something which gives you a n degree of freedom chi square random variable. In that case, we can reasonably understand that this has to be chi square random variable with n minus 1 degrees of freedom. And this is what is our argument. I have written it down again. This is the identity that we have got. This is the same as a previous one. We see that this as we argued before is chi square n minus chi square 1 degree of freedom. This is chi square with n degrees of freedom. Sum of two independent chi square random variable is also chi square with degrees of freedom as sum of their degrees of freedom. It is reasonably reasonable to conclude that the center one is also chi square with n minus 1 degrees of freedom. So, what it says if you look at this carefully, this says that sorry, this says that the s sorry, let us go up again go to arrow. We go back and we use the pen. So, now what we have is remember that this quantity is s square divided by sigma square. And we are saying that this is distributed as chi square n minus 1 degrees of freedom. Here we are saying that s square over sigma square is distributed as chi square n minus 1 degrees of freedom. So, quickly if we see we saw that if you assume that the population distribution is normal distribution with mean mu and variance sigma square, then the sample mean is distributed also as a normal distribution with a mean mu and variance as sigma square divided by n the size of the sample. And the sample variance in that case is distributed as a chi square distribution with n minus 1 degrees of freedom when it is divided by sigma square. In other words, this also shows that expected value of s square, I am sorry here there is n minus 1. Now it makes sense, expected value of s square becomes sigma square, which is what we had shown earlier also. Here there should be n minus 1 because this divided by n minus 1 is s square. So, s this is n minus 1 times s square divided by sigma square. This brings us to another distribution. You remember we introduced a t distribution. In t distribution we said that if there is if z is a standard normal variate and y is a chi square random variable with n degrees of freedom, then z divided by square root of y by n is distributed as a t distribution. Now you see what we have is a z is a sigma that is sample mean minus population mean divided by sample mean variance of standard deviation of sample mean is divided by is distributed as normal 0 1. We call y as n minus 1 sample variance divided by the population variance. Then we know that it is distributed as chi square n minus 1 and therefore this t random variable which we can defined as x bar minus mu divided by s divided by square root n is distributed as a t distribution with n minus 1 degrees of freedom. Please recall, I mean look at a certain similarities, similarities with this definition of random variable and this definition of random variable. You see that when sigma is unknown in future we are going to do that. If the population variance is not known population standard deviation is not known then if you replace it by its estimated value which is sample variance or sample standard deviation then instead of a normal distribution the standardized or a normalized random variable having a standard normal distribution it will have a t distribution with n minus 1 degrees of freedom. Again this is what we are going to use in future with respect to interval estimation as well as we are going to use it with respect to hypothesis testing. So please remember what I have I said is that if you have a sample n sample of size n from a normal distribution with mean mu and standard deviation sigma or variance sigma square then the sample mean minus mu divided by sigma divided by square root n that is the standardized or a normalized value of x bar this is a normalized sample mean that is distributed as normal 0 1 but in case sigma is not known and you replace sigma by the sample standard deviation then the same normalized sample mean with the estimate of or the estimate of a population standard deviation it becomes a t distribution with n minus 1 degrees of freedom. So now let us summarize we first introduced here the standard the sample variance and its expected value by not assuming any form of the distribution we only said that the population distribution is f with a common mean mu and the standard deviation sigma. Then we made an assumption that the population is a normal population with mean mu and variance sigma square then we said that the sample mean is distributed also as a normal distribution with mean mu and variance sigma square by square root n sorry this should be sigma square by n or there is a mistake here please correct it it should be sigma square by n then we found that sample variance is distributed as a chi square distribution with n minus 1 degrees of freedom with certain multiplication please remember and i think i should make correction here also because it gives a wrong impression and this should not happen what we really mean to say is that n minus 1 s square over sigma square is distributed as chi square sorry chi square n minus 1 degrees of freedom please make this correction sorry for this mistake and then we revisited the t distribution by stating that the ratio of sample difference between sample mean and the population mean to the sample variance by square root n is distributed as a t distribution with n minus 1 degrees of freedom next we will consider further values on sampling distribution thank you