2. Making Suggestions in English What do you say when you want to make suggestions in English? This video will give you several tips and phrases to help you get started. Ready? Let's begin. What do you say in the following situations? A friend asked for a suggestion on what he or she should buy. What do you say? Someone asked for your advice on a personal issue. What do you say? Someone asked for your recommendations in a formal meeting. What do you say? A friend asked for suggestions on activities you can do together. What do you say? Your boss asked for suggestions on what the company should do. What do you say? Situation 1. A friend asked for suggestions on buying a particular item. Friend, should I buy the Porsche or the Ferrari? You. What do you say? Think about it for a minute. I think you should buy the Ferrari. Why is that? Because I'd like to borrow it. The easiest way to make a suggestion is to say, I think you should. You can also say, maybe you should buy the Porsche. Do not say, you should. This is too strong for a suggestion. It sounds like you're telling them what to do and people don't like to be told what to do. Also, do not say, you had better. That sounds like a warning. If you don't do this, something bad will happen. Tip. When making suggestions, keep it light. Don't be commanding or demanding. Words like, maybe you should, I think you should, help soften the tone for you. For example, I think you should stay home for a while. Maybe you should try meeting new people. Maybe you should go online and find more information. Negative suggestions. In English, we make negative suggestions differently than they do in other languages. We usually say, I don't think you should buy the Ferrari. In other languages, people might say something like, I think you should not. I know, that seems more logical, but it isn't as common in English. Situation 2. A friend asked you for advice on a personal issue. What do you say? Should I get a new hairstyle? What do you say? If I were you, I wouldn't do it. You look great the way you are. When someone asks for personal advice, you can put yourself in their shoes.  Also, you could speak hypothetically, which means imagine the situation. Maybe you could cut it a little shorter. It might be a good idea to let it grow longer. Negatively phrased questions. A strange but common way to make suggestions is with negatively phrased questions. The question is actually a positive suggestion. Why don't you shave your head? This actually means, I think you should shave your head. Why not dye it a different color? This means, maybe you should dye it a different color. Someone asked for your recommendations in a formal meeting. Colleague, what do you suggest? What do you recommend? What do you say? In this case, you can directly state your suggestions. I recommend that we advertise on social media. That's a great idea. Any other suggestions? What about holding a big event to promote our products? In these situations, you can sometimes speak hypothetically. What would you recommend? What would you suggest? I would recommend doing a customer survey. Sounds like a good idea. In some meetings, a more informal approach is fine. What are your ideas on this? Or do you have any suggestions? I think we should assign that to marketing. Or it might be a good idea to hire an advertising firm. Situation 4 A friend wants your ideas on doing something together. What do you want to do this weekend? What do you say? In this case, change the pronoun to we. I think we should go to the ball game. Maybe we should take a road trip. Why don't we go ice skating? You can also say simply, Let's go bowling. Why not catch a movie? How about going swimming? Situation 5 Your boss asks for ideas on what the company should do. What is the best way to handle this? What do you say? Use we to make suggestions for the company. You are part of the group. I suggest that we hold a press conference. I recommend that we hold a press conference. Or maybe we should hire a public relations firm. Note, we have another video on making formal suggestions and recommendations. Check it out at the link below. Making Suggestions To Recap Here are some phrases for giving advice or suggestions to another person in informal situations. I think you should. Maybe you should. Why don't you? Why not?  It might be a good idea too. I don't think you should. Suggesting an activity together. Here are some phrases for giving suggestions for a shared activity. I think we should. Maybe we should. Why don't we? Why not? How about? Let's. In more formal situations. For example, in business meetings. You might say something like this. These are more formal. I suggest that we. I recommend. My recommendation is. I would suggest. Also okay in some meetings. This is less formal. I think we should. Maybe we should. We could. What about? Practice making suggestions in the following situations. Your friend asks for advice in choosing a pet. Your classmate asks for suggestions in doing an assignment. Your coworker asks for recommendations on a particular project. Your boss asks for recommendations on what the company should do. Your girlfriend or boyfriend asks for suggestions for a weekend activity. Your friend asks for help with a personal problem. Your mother asks for ideas in decorating the house. Your roommate asks for advice about choosing a major. Your brother or sister asks for advice in dealing with teenagers. Think about these situations and role play. Some of them with a partner. I think you should take more time on this. Feel free to pause the video and practice these situations together. Let's talk. I think you should. Go ahead. Think of some situations and make suggestions. Take as much time as you need. Hope you enjoyed that. If you liked the video or learned something new from it, why not give it a thumbs up in the comment section below? And how about subscribing to our channel? Thanks for watching. If you have any ideas for our next video, maybe you should send them to us at the link below. Just a suggestion. This video was brought to you by the following English Learning websites.


Welcome to the show. It's me JP. I got excited about the song today song rocks What's happening? Hey welcome. It's time for JP's product pick of the week right here in my workshop It is Tuesday. That's where we are. It's one o'clock eastern time. No, it's one o'clock Pacific time four o'clock Eastern time. That's when this happens And hello, hello, hello to the people over in our chat Hey Jim and Jim Hennickson Mike P thin man see Grover. Glad to see you We've got people over in our YouTube chat as well tackle the world David S. Charles Burner for Jeff Hunt Bill Ferguson is this YouTube? Yes Batagraph of Delhagen. Hello, and thank you for stopping by if you're wondering Where the chat is if you're over somewhere in Twitch land or LinkedIn learning or periscope if that still exists Vimeo Do they do live anyway? The chat is actually happening over on our discord so go over to adafru.it slash Discord look for our live broadcast channel live broadcast chat channel. I should say it looks Like that. That's it right there. In fact. Hey blitz city DIY. Hey Exclamation point evolt now we I want Love exclamation point. I'm gonna guess is your handle backwards. Hi Be the dude creative. I Derek Treywick over in our YouTube. Hello So What's happening here today? I've got a cool new product pick if you want to jump over to the product page for the product pick And take a look Sneak peek. That's the product ID right there 4481. That's all you need to know But you can use that URL. You can use that QR code. Those will all get you there Adafru.it slash 4481 will get you there. That's our little sort of URL L shorten her Hey, Todd bot also just joined our chat Head over there because this show is happening inside of that product page And we're excited about that that you can watch us right in there You can read the copy. You can click the links. You can throw some in your cart for a Tremendous discount. It's a great deal. It's 50% off today for this mysterious product that I'm teasing But before I get specific about it, I'm gonna let Lady Aida get specific about it. How about that? It's the itsy-bitsy nr 52 840 So the itsy-bitsy is is this kind of form factor that we like using it to go 0.7 inch by 1.4 inch size and It has a micro USB and one end and then it has a whole bunch of stuff inside that makes it easy to use with Our Arduino or circuit Python in this case. It's an nr 52 840. It's a USB Capable Bluetooth le radio module which just about the module just got FCC see italic certification everything and then It's kind of big so we had to use the bottom so it doesn't sit flat like the other itsy-bitsies But it has two megabytes of SPI Q spy flash has a dot star RGB LED. It has a 32 kilohertz crystal. It has like power regulators and stuff And it has nearly identical pin out to the other itsy-bitsies the biggest difference is of course There's no pins on the end usually there's like another extra five pins where that antenna is But then ten is there and even if we know we did move the module over you wouldn't want those pins You know that much metal near the antenna And so we just kind of pushed at the end and then you have all the connectors that you need along the sides including Pin five which is a special pin. It's level shifted up to five volts So it's an output only that means though that you can use it for driving a neopixels directly Or if you ever need something that needs five volt power logic You can use that pin for that. So this is great for very compact Bluetooth projects are smallest VLA module It's the teensies one yet, and it's got two buttons one for Bulloader and reset and then we have an extra LED for a user switch Why put it there? I don't actually remember why but at the time it seems like a good Actually, I was thinking like why did I put it there? But you have an extra switch so maybe if you want to you know some people are using this for keyboards Maybe you switch modes or whatever it has a little you know button on it. So it's very small Compact but once circuit Python beautifully once Arduino beautifully you can use it with all our recent Circuit Python library work and of course all the historic Arduino libraries that we've written over the years Yes, yes indeed it is Where to go? Hey, look, that's it right there Dun-dun-dun shake that out of the little ESD safe pinkish bag. Ooh, right right on Let me let me bring this up here on the main camera. This is it This is the product pick of the week this week. It is the itsy-bitsy nrf 52 840. I love this board These are great. First of all lots of love for itsy-bitsy. It's just a nice size It's not too small. It's not too big. This does happen to be the smallest board We make that uses the nrf 52 840 from Nordic semiconductor. This is a Bluetooth le BLE capable microcontroller Which makes it perfect for all of your Bluetooth le projects such as doing stuff with fancy light bulbs doing stuff with iOS devices I think you do stuff with Your Android devices with it. I've done stuff in Mac OS over BLE Bluetooth le Bluetooth low energy with it It runs in both Arduino and circuit Python. We've got libraries to make it easy easy easy to work with We have a bunch of example code and a bunch of example projects for using this under both Arduino and circuit Python and I wanted to first of all, let's let's take a look at Bring up that product page right there. So there it is. That's the Product page for this one here today. It's product 4 4 8 1 Half price right now during this show only so you don't need a coupon code or anything Just throw it in your cart for that price nine dollars ninety eight cents us limit of ten per customer no resellers, so just actual Normal customers. That's normal. You can get up to ten of these. So if you have big big BLE project dreams, this is the one for you Excellent little board and we've got if you scroll down here, you'll see there's a little description Some bullet points about it including things like we have 1024k flash 256k Ram 2 megs of Q spy flash on it Which is great for your circuit Python projects for storing assets and code What else it has 21 GPIO pins on it six of them are 12-bit ADC pins You can read analog inputs on it such as the universal symbol for analog input a potentiometer knob being twirled Also has up to 12 PWM pins if you want to write out things like Pseudo analog LED values. It's perfect for that. Now. It's also got hardware SPI UART I squared C I to S for your digital audio output needs and if you keep scrolling down You'll find a link that takes you right here Which is the main guide for that to be seen or a 52 840 express This has some general info. It has the ever helpful pinout page That's that's the critical page right there. You can go and take a look at the nice big Pinout diagram there you can blow that up to full size if you hit that Original link there that gives you the full-size one. You can usually zoom in even further now. It's super big Suitable for printing and framing if you want or just keep it digital And that'll tell you the uses for all the pins the one Super sneaky special secret fancy funny pin on this is the D5 pin Let me go back to This image of it right here. You can see the pin Five there has a little exclamation point on it and a little extra line on the Output pad there on the silkscreen That's to let you know this one has been level shifted up to five volt logic So it's an output only pin on five volt logic. You can you can grab five volts off of USB pin there if you want and That's perfect for things if you happen to have sit maybe some neopixels that are not Working nicely with three volts, especially older neopixels. They really wanted the five volt or other devices where you really need five Logic this one has it on there, which you don't find a lot these days a lot of boards tend to be three volts Across the board. So this is kind of a nice little special feature there And it is an output only pin no input on that one Also, this is running on the Cortex m4. So so the nr 52 840 is a chip that's on the Cortex m4 Architecture, but it also has the built-in Bluetooth built in USB. You can use it as a USB device for things like MIDI and storage and HID if you want it to be a keyboard. It's great for stuff like that I have kind of a neat project here something I like that I put together That I want to show you. Let me switch switch camera views here And let me bring this guy Into view here. So here you can see I have a ginormous mechanical key switch Let me move the side image and make it a little smaller so that we can fit more on the screen here And I'm gonna try to just fix that Loan out exposure. There we go. So you can see I have our Itsy bitsy nr f 52 840 bolted to the side here. I'm just running a ground and one input pin to The switch contacts there and then I'm running it to USB for power. It's also so I can show you the code on this but The idea behind this is when I am listening to a podcast Or music on my phone Especially I find with earbuds in And then I suddenly need to pay attention to something. I'm often fumbling into my pocket to find the phone and hit pause Live demo including wireless stuff. So let's cross fingers. But this is programmed to act as a Uh, what do we call it? HID consumer control, which is things like play and volume over bluetooth le to the phone. So the phone here No wires attached, right? This is this is just a phone Right, so you're rocking out to your tunes and then someone needs your attention. Something needs your attention Boom hit the big button that just sent bluetooth radio wave youls across the ether into The phone and the phone by being paired to this in bluetooth mode I can zoom out a little bit more make it look a little more obvious what's going on here Like that, uh, watch the play button there. It's playing It's pausing now you can do all sorts of other things over the bluetooth You can do pretty much all of the transport controls next song scan ahead Volume stuff there's a lot you can do but I find the the the most critical one is I just need to Pause this thing Because someone's trying to talk to me and I've got earbuds in and I just whoa So that that's the project there and it's all running right on that cute little Itzy bitsy nrf 52 840. Uh, let's take a look at the code there. Um, if we Jump over to this view and get rid of the extra Uh camera view there you can see here, uh, I've got this coded in circuit python and this is based off of one of my learn guides I did on making a Knob using a rotary encoder on the circuit playground blue fruit which also runs the same chip So if you find projects on the circuit playground blue fruit if you find projects using The feather nrf 52 840 Uh the clue these are all using the same chip. So a lot of the code will be Transportable between them key stuff going on in the code here is that I've got the ater fruit hid library with its consumer control And consumer control code. That's the stuff that sends things like play and pause Uh importing ater fruit ble And then I am setting up the ble radio. I'm actually calling it blue fruit pause button. That's just the name I gave this so in fact if I go back To my Bluetooth settings here Adjust the exposure down a bit Uh, you should be able to see there's a item i'm connected to called blue fruit pause button and that's that's that uh Gizmo right there that that i'm hooked up to Then what we're doing is advertising that uh that blue that hid name Over blue fruit or over bluetooth i've set up two buttons actually i'm using The big button there but actually just for testing purposes I also used the little On board button. So uh as lady aida mentioned she put a button on here. She couldn't remember why well This is why so you can test stuff like One of your buttons without having to actually hook something up to it Which I love I love when microcontrollers have one little spare user button on there It means you don't have to just grab a piece of wire and and short to ground Or or hook up an actual button for just just just one button very helpful to have that built on there So thanks. I'm glad you did it Let's see what else happens. Yeah, so I've got the two buttons set up there Uh, and then in the main loop what we do is we check to see if we're connected and we kind of hang out once we do Uh connect we can move on with life continue on in the code and then all i'm doing is a couple of Checks for the button and the key switch And this is the whole command right here cc send consumer control code play pause and it's the same command Uh, and there is no notion with these of state So it doesn't know if it's playing and now i'm about to pause or if it's paused and now i'm about to play It's just a toggle that flips the state of that. Uh, and that's to prevent you from getting into weird circumstances where you've Started it on the device And are trying to stop it on the micro controller. So it's it's the same command, which is uh, which is nice um Let's see this uh This Big humongous button by the way, I love these we have them in the store It's called the kale big mechanical key switch. This is the clicky pale blue one. Um, you can see it has a huge Key cap on it Right there you take that off it's still Works as a button this one makes a lot of noise because it's clicky and then I just designed a little uh, three printable stand to set that on so, um, I think we have some guides. I think the reese brothers and uh Did I do one? No, I don't think I did. I think the reese brothers have a have a guide where they've made, uh, these switches Um a little stand for them. So you can probably look for that if not I can post This designer a similar one. All right pause that again uh And let's see What else any questions, uh that anyone has let me know over in the chat. This is uh, there's the product page I'll throw that back up there Uh, neat thing is that it looks like the r52 series is supported by radio head library So it could be used as a short range 2.4 gigahertz radio. I had no idea you could do that. Oh, that's really interesting. Thanks. Uh, Heel pie I've used that for some of the other Um, other rate like laura radio and some of the other radio stuff, but I didn't know you could use that with this one Um DJ devon trying to figure out if this is going to be a ble synth io thingy Uh, well, I don't know about that, but it could certainly be a cool controller for that. So yeah, that's a neat I hadn't thought of that at all. I should say so thanks for throwing the idea out there Uh, keel keel pie says a 40 percent ortho linear would be hilarious with these keys. Absolutely. I think we have 50 Of them in stock or something like that. So if you really if you want to go crazy with the huge buttons Fun to type on uh, let's see Any other thoughts or questions over in the chat? Um I think that covers it. Did I hit everything I needed to say? Do you have questions because that's the that's the thing It's the itsy bitsy. These are great. They're smaller than A feather they're bigger than a cutie pie or a a trinket Um nice size lots of gpio on it, which is great. It's a good good size because of that very similar to our kb 2040 it's also in that sort of um Pro micro to smaller teensy sort of form factor these little sort of 21 ratio rectangles with a bazillion gpio on them really nice. We also by the way Have some accessories for these you of course can can solder pins to them put them on breadboards or perma protos We do have a backpack that can go on it that gives you a lipo battery charger And and connection so that starts to me that starts to get a little bit over into the feather world So I particularly like these for projects where i'm uh keeping usb plugged in it's it's real convenient in this case There's no reason for this thing to um To run off of battery, but I don't have to plug it into the phone So so the fact that we have wireless means it can talk to some device you don't want to be plugged into but Running it off of usb works great to just have power on that all the time Yeah, so we do have some accessories you can plug these into so look for those I know c grover has made some adapters I believe to let you use some feather accessories, uh with these some feather wings into The uh, the itsy bitsy form factor. He's a he's a big proponent So look for c grover in our chat and uh, and you can follow the links to some of his Github to see some cool add-ons for that um And uh that I think Does it yeah ble always have handy to have I I absolutely agree All right. Well, I think that's gonna do it then for today Uh, thanks to everyone for stopping by that is my product pick of the week this week It's the itsy bitsy nrf 52 840 Go get some Freighted fruit industries on john park. It has been JP's product pick of the week and that's it right there. So go get yourself some no discount coupon or code or puzzle to solve just Get them at that good good price nine dollars 98 cents half off right now till about Now about the end of the show uh, once the show is up the price will will jump back up to the original Within a few minutes probably so Go grab some stuff throw throw it in your cart and uh, check on out Thanks everyone. I appreciate you stopping by and I will see you next time Bye-bye


Jadi hari ini saya adalah seorang seorang seorang seorang yang berbicara. Saya rasa untuk membuat aplikasi reka dalam dua minggu adalah... ...sangat hebat. Kita mempunyai satu buah bulan selama 8 minggu dan dua minggu sangat tidak percaya. Jadi setiap hari, setiap hari, tetap. Saya adalah seorang wanita tank. Macam mana saya boleh lakukan ini? Jadi hari ini saya akan bercakap tentang kecewa yang kita belajar... ...semasa kita belajar sebuah bulan selama 8 minggu... ...untuk aplikasi reka yang digunakan dalam hidup sebenar. Ini menghubungi sedikit tentang apa yang Loxie bercakap tentang sekarang. Macam mana kita berkongsi model yang berbeza bersama. Jadi hari ini, kita akan pergi ke zoo. Jadi... Saya tidak pasti kenapa saya panggil kebinat... ...tapi kemungkinan itu adalah zoo... ...dan kemudian mereka berjaga-jaga dalam kebinat. Saya akan beritahu. Ini tidak akan menjadi sebuah teknikal. Ia akan berlaku seperti sebuah permainan atau sesuatu. Ia akan sangat terang. Saya akan beritahu bahawa orang di sini... ...tidak akan berubah. Jadi ini adalah sebuah kes yang digunakan. Jadi ingat jika ini adalah zoo... ...dan zoo mempunyai banyak kebinat yang digunakan dalam kebinat. Jadi setiap kebinat hanya dapat menggunakan sebuah kebinat. Oleh itu, mereka akan mulakan memikirkan satu sama lain. Kemudian setiap kebinat dapat digunakan dalam beberapa kebinat. Jadi bagaimanapun, dalam kes ini... ...dia akan mempunyai 3 kebinat dalam sebuah kebinat... ...dan kemudian kemudian kebinat yang berbeda di D. Untuk orang yang tidak terlalu terlalu memperkenalkan... ...setiap kebinat menggunakan sebuah kebinat... ...dan setiap kebinat mempunyai banyak kebinat. Dan itu adalah cara menggunakan asositi antara kebinat dan kebinat ini. Jadi dalam kes ini, ini adalah sebuah kebinat dengan kebinat saja. Jadi anda dapat mencari apa yang ada di kebinat... ...dengan mencari kebinat dan kemudian kebinat. Kerana sebuah kebinat yang anda mencari, menghargai kebinat. Dan untuk setiap kebinat, setiap kebinat yang ada di kebinat... ...dia dapat mencari kebinat yang mereka menggunakan... ...dengan mencari kebinat. Dan itu juga sebab anda mencari, ada banyak kebinat di sini. Tapi anda tahu, dalam kebinat, anda mempunyai beberapa kebinat. Jadi di setiap kebinat, anda masih mempunyai kebinat... ...dan anda dapat mempunyai kebinat juga. Tapi anda tahu, tidak ada sebuah kebinat atau sebuah kebinat. Jadi anda menganarakan kebinat ini dulu. Jadi dalam kebinat ini, bagaimana anda menghubungi kebinat... ...dengan sebuah kebinat atau kebinat? Dan anda tahu anda dapat menghubungi kebinat, kadang-kadang seperti ini. Jadi dalam cara kebinat, ia harus dikumpulkan... ...sehingga kadang-kadang kebinat dan kadang-kadang kebinat. Jadi anda menghubungi kebinat anda... ...dengan cara menggunakan kebinat yang mereka nampak. Jadi kebinat yang menggunakan kebinat... ...beri anda dengan cara ini. Jika anda menggunakan... ...jika anda mempunyai kebinat, anda akan menulis tekanan... ...dan anda menggunakan sebuah kebinat ini. Bagaimana anda dapat menggunakan kebinat? Bagaimana anda dapat menggunakan kebinat? Apabila anda menolak kebinat polimofik... ...saya tidak yakin anda menggunakan sebuah kebinat yang betul. Kemudian anda akan menerima bahawa... ...dalam kebinat model... ...dia akan mempunyai sebuah kebinat... ...dengan sebuah kebinat... ...dan sebuah kebinat yang berpengalaman. Sebenarnya anda dapat melihat... ...puan dan sebuah kebinat... ...saya ada dua perkara yang berlainan. Kerana kebinat yang berlainan... ...bukan bila ia bergurau atau berlainan... ...atau kebinat yang berlainan... ...atau bagaimana kebinat yang mereka ada... ...atau bagaimana anda menghubungi kebinat atau apa-apa pun. Jadi, apabila dua model... ...punyai kebinat yang berlainan, anda tidak menulis... ...dan berlainan dengan kebinat. Kemudian dengan pilihan yang berlainan dan pilihan yang berlainan, pilihan yang berlainan adalah tersinggung... ...dengan kebinat A atau P. Apabila anda menulis itu untuk menentu kebinat, ...atau anda akan mencari kebinat dengan pilihan yang berlainan... ...dengan pilihan yang berlainan, seperti 1. Jadi, pilihan yang terlebih... ...kenapa, mempunyai kebinat yang berlainan dengan pilihan P. Jika pilihan yang berlainan adalah 1, You look for in the plant model, the first data in the plant model. So in this case, cabinets can take up, can be linked to two different models. And then the association will look like this, where cabinet belongs to occupiable polymorphic truth and then an animal can have many cabinets, but this time linked to S occupiable and it goes back to the cabinet over here. I think a lot of it is like how you write things and recognize the patterns of that. So this is just part of the syntax. So instead of like before, when each cabinet can only have animals, here you can have either plants or animals. And then when you, just previously, when the cabinet only can have an animal, you call it ad cabinet dot animal, but this time it's associated to occupiable instead. So when you call ad cabinet dot occupiable, the data retrieves either a plant or animal depending on what occupiable type is. And then with that particular animal itself, if you call it ad animal cabinet, then it retrieves what cabinets is this particular animal can be found in. Similarly for plants as well. So the Rails console, if you can test, actually you can just use the Rails console to test how this data is like saved and retrieved and you just find out how to retrieve all this information. You can test your methods over here. So say for instance you have a plant that's a rose, that's a first. So you save it in the variable plant and then you call which plant dot cabinets to find out which cabinet they are found in. And in this case, the array returns nothing, so it's not found anywhere. If you do like plant dot cabinets dot create, it will create a new record of a cabinet called b2. And then it will return instead of nothing, a record here that says, okay, this is the creation of the cabinet itself with the name b2 and the occupable ID1, which is this one here and with the type plant. And then if you go back again to look for plant dot cabinets, it will return you an array with the cabinet that you just assigned it to. And if you create it again, like you do this again, you say like b3, then there will be two records here. And okay, so that last, there's another way of retrieving that information because it's linked both ways, has many and then belongs to. So with the last cabinet just now that you created, cabinet dot last, you do cabinet dot occupable, it will retrieve that plant ID with the name rose there. And here it's not an array, but it's the record of the plant itself because a cabinet can only have one plant. And then if you call the attribute of this occupable, which in this case, you know, refers to a data point of a plant, it will get you rose here and if it's green, this occupable, which is a plant, will return you true because roses is a green plant. Okay, say for instance, you have a cabinet 12 and right now the cabinet is empty. Okay, that's why you see like occupable is new and tight is new as well. And then you assign animal to the last animal and then for the cabinet you just defined in on top, you update with the occupable attribute animal which refers to this snake here. And then you update that particular cabinet itself with the snake and you call it name and the snake will come out here. So, maybe I'll do a little demo of what it looks like on a... Okay, so it's just a very simple view here. Okay, so if the cabinets are arranged like this and you realise okay, the top level should be all plants instead of like a rose and a tiger. So maybe the top row you want it just be like just at plants, right? You can select a plant here instead and then you save the changes. And then you can assign where things will be like this. So, you can see all the plants are on top and then all the animals are below and that's how a cabinet is linked to a different model, either plants or animal here. I mean, this is not a very good example with the animal and plants thing. Okay, so there's a feature that Konrad was supposed to present on and there's single-table inheritance. So, I'll just touch a bit more on what's the difference between single-table inheritance and polymorphic associations. So in single-table inheritance, okay, this is a lot of words but let me just put it in like more layman terms. Usually, why will you use single-table inheritance instead of polymorphic associations is when you're referring to the table itself. It's nothing to do with associations on its own. So, for example, a user, a user can be a customer, a seller, or say admin. So, it's kind of like defining different roles but it shares similar attributes because they're all people. So, say, the user can have an email address, password but say, for example, admin has certain attributes that are specific to them but generally, they share similar attributes and overlapping ones, not necessarily all the attributes. They don't necessarily all the same attributes but they have a lot of overlapping ones and that's when they use case, you use single-table inheritance but for polymorphic associations, it's more sort of how the different models link to each other. So, for example, you have a calendar and you have an appointment and you can link the appointment to a person in your database or a company in your database and a company and person takes up very different attributes, like a company, maybe you're a market capital and then the person maybe you can market capital as well but the attribute will be different. So, in that use case, you wouldn't put companies and models together because the attributes would be totally not overlapping at all. So, that's it. I'm not sure whether it was magic or just confusing. Can I ask the J-Work? What's the false cascade thing? False cascade. Like the database. This one? Yeah. False cascade.  Ya, cool stuff. You can see the different attributes that each model has in a long list and all that. So, this is just what it would look like in the schema which tells you what models you have and what attributes those models have. So, occupiable is actually not a table. Is it a table? No, it's not. I can't find the scientific word for it or like programming word for it but it's kind of like you imagine linking these models through something else. So, it's kind of kind of the medium of vehicle. Ya, to draw the relationship. Ya, so, like the cabinet is linked to the occupiable and then the occupiable is linked to animals and I think it's clear when you see it this way. Ya, because it goes like this way. Ya. So, it's like a table but not a table. It's like an imaginary table. No, no, no. That's not a table at all. It's kind of like a name that you call it by so you can link it to another table that has that name. Ya. It's going to go on YouTube, right? Ya. Ya, any other questions? Cascade. Force Cascade in every app, right? Does it come with it or is it something that you can't think of? I think Force Cascade is nothing special with it. Does it come with it? So, the answer is no long. Ya. I'm quite sure I'm not sure. Ya. It's a database thing. So, I'm not sure about movie. What cascade means is that because you got three tables, right? Or which the data link. If you put cascade, if you delete the data from one table, if you delete the one that's linked, where? If you don't delete, that means you get some data that has stuck because if you delete one side, the other side, the best link gets stuck. So, if you put cascade, you will delete the one that's linked. When you create a table, do you create a migration? Do you use references? Yes, I did. So, it creates a foreign key constraint because it creates a foreign key constraint which links these two tables together. Ya. So, if you delete one without deleting the other or removing the link, it will prevent you from deleting anything. So, if you delete a record, say, from animal, it will prevent you from deleting it if the cabinet has the animal. Ya. So, if you delete the other one, it will prevent you. Ya. Okay. Ya. Ya. I need to... For example, if you delete in cabinet one, the one, maybe let's say, flower and if you delete one, then the flower all goes together. You cannot just delete flower and record the link into three tables which will be left to get that. If you're missing one, it's a record. I can't just say a lot of people the data in one of the tables without deleting get it, you know. Because of this, it can cause the result as well. So, do I have the reference to point to something? Ya. Okay. Wah, that's something new. Thank you. Thank you so much. Ya. Does anyone have any other questions? No? No? Yes? No? The use of the last slide SDIH What's the use? Okay. Okay. Let me see. Ya, so, I was saying okay, the thing is, like in this case, I was saying like with Polymorphic Associations, right? You are trying to associate like one table with two. Ya, but for single table inheritance, right? It only refers to one table. It's nothing got to do with what it relates to. Ya, so for instance, I was saying like a user here, like a user here can be like all of us. And then, like, you know, or like maybe a group of us has like specific role like she's admin. And then the rest of us are all like customers.  And then maybe use an integer. But instead, right, you can if you use, if you call her admin there are like whole group of admins here and then like the rest of us are like customers. It actually allows you to do certain features like you can put admin. Admin, like capital A, admin. So it retrieves like information from that. Am I wrong? Am I wrong? Ya. So for single table inheritance and Polymorphic Associations, so for Polymorphic Associations, as she was saying, you have two fields. You have the idea and the type. So the type actually identifies what table you're looking for, the ID, identify to record ID, which record to retrieve. So use Polymorphic Associations when you actually want to interact with, so let's say for example you're in voice class and you want to interact with what you call available. So available can be a company, can be an individual, can be whatever but you're interacting with it the same way. So you use a Polymorphic Associations I can put in be a company, be a person, or a task into this association and I will interact with it the same way as available. But STI is, let's say you have different models but they more or less share most of the attributes on the scene. So you have additional columns to store attributes that maybe one model has that the other doesn't but since most of them are overlapping, it isn't necessary to split up into multiple models. So you can actually have different models but all referring to the same people. So you save a lot of database space as well depending on how we implement it. So the use cases are probably different in this case. So Connet was supposed to cover STI but she wasn't here. That's why there might be a bit of confusion. Okay. So let's say there is this actually done during runtime as an object so it doesn't necessarily use a database. I mean when you overload the attributes of a particular class you don't actually extend the data to display it to itself. So is that useless? So for STI let's say you have multiple models but for example at the end of the day it's not stored in a database. Yes, it's not. It's not. So your explanation was but this time the overloads are not going to be stored in a database because we are talking about classes or objects. So they will accept it for example. Okay, we're going to stop it now.  Do you want to listen to the debate? Yes. You were expecting a chicken like that, right? We want to expose it. I don't think there's a trope in programming. There is. I'm not sure. We can fight about it later. Yeah. Let's talk about it now. No, let's not do that. Okay, so any other questions? Yeah. Let's just start the debate. Yeah, but anyway I think all this is very healthy. We are all beginners and I come from a background that's like non-technical at all. So what are you doing for three months? So thank you. I think it's a lot of peer learning and all that. And you should tell me that I'm wrong because I should know now then later. So thank you. Yeah. Thank you.


So, now the last topic that I want to consider in this course is applications to reliability theory. That means again the concepts that we have learnt during the course of probability theory, I want to show you some applications. Of course, everything may not be very new, but still we want to put them all together. So, that you have a good feeling about and of course, see the reliability theory is a very, it is become very important now with since the systems very complex systems, you know coming in and then besides that you know you have lot of dependence on the systems functioning. Otherwise, if something fails then lot of things are connected with it also fail and you know there is a chaos. So, this is a very growing area and we see that the applications are really interesting and very meaningful. So, you can model situations here also through the tools that we have learnt during the course. Now, so first of all let us first understand what we mean by reliability of a system. Now, just for example, consider steel beam under load and so you have whole structure you know resting on a beam and there is a heavy load, then you have a fuse inserted into a circuit, so the source of stress. So, you know there are systems and then there are some source of stress. So, here and for example, an aeroplane wing, the planes fly at high speed, there is lot of friction and so there is some sort of stress on the aeroplane wing also, then electronic device you have, this is when it is functioning again that is called that is a sort of a stress and therefore, so one can go on and writing a number, the list can be very very big you know anything that you use as a tool and then so when you are using it, there is some stress, some kind of stress on the tool and so things will change or things will happen. So, that means, so you have a source of stress, you have a system that means a component or a whole system and then you talk of state of failure. So, what can happen the beam can crack and similarly, a fuse can burn out or the aeroplane wing can buckle because of pressure or stress and an electronic device can just fail. You suddenly find that your PC is not working or your you know electric kettle is not working or whatever it is right. So, therefore, you know you can write down your own these things, you can take a component or a system, you can talk about what kind of stress that system is facing and then you can also define the way the system will stop functioning. So, essentially what we are saying is that we have this. So, now here we can and suppose we I define therefore, so we need to talk about time to failure or life length and it will be a random variable and why because you see if you take identical components under identical stress may fail at different and unpredictable times, you really have no idea sometimes a thing just stops working. So, some may fail early, some may fail at later stages and so on. So, therefore, you can see that whatever the systems we have talked here and talked about and many other, you see that you cannot really for sure say that this component or this system will work for so long. So, there is lot of unpredictability if they are not. So, these things can not be predicted very well and therefore, because the you never know how the stress works on a particular component or a system and also the manner of failure also varies as I told you because the beam will crack, the fuse will burn out and so on. So, the manner of failure you can say fuse working one moment will fail the next moment, you suddenly you find that thing is not working, you are having good output the radio was functioning very well broadcasting and suddenly it goes away goes out. So, the beam you know steadily over a long period it becomes weaker and weaker and then it cracks. So, here again and many other situations you can talk about. So, therefore, it is reasonable or it is appropriate to construct a probabilistic model and then treat the lifetime of the system or the component as a random variable. So, this seems to be very appropriate and now we will what we will do is we will talk about different models that we can use for predicting or for the lifetime of a component or a system and we will be using lot of tools that we have learned so far. .So, first of all let us define because now with the understanding that what we mean by system failing and the manner of failure can be very different and the unpredictability of these components or systems failing under different situations. So, we can now define a reliability of a component or a system at time t say by r t. So, we will define so r t will be the will define the reliability of a system and we will say r t is equal to probability t greater than t. So, at time t we want to know the reliability of a system then this is equal to probability t greater than t where t is the life length of the component. So, suppose that we are talking about a component then t is the life length and we want to know the probability that t will be greater than t and r t is defined as the reliability function. So, this is the reliability function and so about different values of t we can get the value of this function which will tell us the probability that the system is functioning at that time. So, essentially when we say that r t when we are computing this way this probability. So, if t is the life length that means here it is saying that the life length is more than t. So, that means at time t when you are computing this the system is functioning. So, the probability is not 0 well I am not saying that I am saying that the probability that t is greater than t that means the life length is greater than the. So, the system is still that is how you will interpret this because this is the life length. So, the life time of the component is greater than t. So, at time t that means it is functioning the system is functioning. So, this is what now for a particular item suppose r t 1 is 0.95. So, at time t 1 you compute this and it turns out to be equal to 0.95. This means that approximately 95 percent of such items used under similar conditions will be functioning at time t 1. That is what we mean. So, there are 95 percent of the items will still be functioning will be functioning at time t 1. So, this is what we mean by probability being 0.95. So, probability that the life length is more than point is more than t 1. So, this here this you will write as equal to probability that t is greater than or equal to t 1 for t greater than t 1. So, that is equal to 0.95. So, this probability is 0.95 that means 95 percent of such items under similar conditions will be functioning at time t 1 and we continue with this. So, you see we saw that if f is the pdf of t the random variable t the probability density function. So, in that case we can write the reliability function r t as t to infinity because remember this is probability t greater than t. So, therefore, this will be the integral of f s from t to infinity. So, because we were saying that this definition tells us that the reliability gives you the probability that the system is functioning in the interval 0 t. That is it is not sorry the way to say it is that the reliability tells you that the system is functioning is has not failed in the interval 0 t that is the better way to put it right because the life time is greater than t that means the system has not failed in this interval right. So, it can fail anywhere in the interval t to infinity that is what reliability is right probability t greater than t. So, that will be written as t to infinity integral of f s from t to infinity which if capital F as we denote the capital F as the cdf of cumulative density function of t then this is 1 minus f t right. So, this is what we can express the reliability function as. Now, we will associate another function with reliability and which is with the random variable t which is the failure rate z and this is also called the hazard function. Now, if you recall while talking about exponential distribution I had introduced this hazard function and of course, we did not talk much about it only I simply I showed you that if the pdf of a random variable t is exponential negative exponential then the hazard function will be a constant. And so, we will see many more interesting kinds of hazard functions and but anyway we had come across this at that time, but now I am using this. So, that is why I said that some of the things which I talk about here may already have been discussed, but we are putting them all together. So, that it becomes a complete unit. So, now failure rate we are defining as z t is equal to f t upon r t.  So, if f t is equal to 1 that means and so this will say that the life time is less than or equal to t. So, if this is 1 then this that means it is a certain event f t equal to 1. So, f t equal to 1 implies that by time t the system has definitely failed, it is a certain event right. So, therefore, this has meaning only when the system is still functioning and therefore, this is a reasonable condition to impose that this is defined for f t less than 1 because f t equal to 1 would mean that the system has or the component has failed. So, therefore, so this is your failure rate and why is this, why are we calling it as a failure rate? This is the definition, but now let us understand why this does covers the failure rate of the system. So, consider the conditional probability t capital T lying between small t and t plus delta t given that capital T is greater than t. So, since I am asking for see the failure rate has to be after time t. So, here you have to consider the inequality strict inequality, I cannot allow equality here because my conditional event is that t must be greater than t. So, that is why you cannot write less than or equal to here. So, this is what we have to consider, I mean what I am saying is that the event 2 should be described properly. So, then the probability this less than or equal to t lying between. So, this is strict inequality and that is less than or equal to t plus delta t. So, then by our rule because this and this when you take the intersection actually means just this event because capital T is greater than t already satisfied which is here. So, therefore, this conditional probability can be written as probability capital T between small t and t plus delta t divided by probability t greater than t. And this integral form if I take f to be the pdf then this would be my failure law then this would be t to t plus delta t f s d s divided by r t. Now, for small delta t you see I can take this to be by the mean value theorem or here you do not need small delta t. So, by the mean value theorem of integral calculus this integral can be written as delta t the length of the interval of integration into. So, there exists a value point real number psi between the interval t and t plus delta t such that this integral can be written as delta t into f psi. So, this is the well known mean value theorem of integral calculus divided by r t.  So, then I can because my if delta t is small then this interval is very small. So, I can treat this as the value at t and therefore, this will become f t because if this interval is small then your psi is close to t and so approximately I can say this is equal to z t into delta t because your z t is f t upon r t and so this is what your and therefore, z t represents the proportion of items that will fail between t and t plus delta t. That means, during the time span delta t so this is the proportion of items and that is why we call it the failure rate. So, among those items which have not failed till time t remember because we are computing this. So, this is p t greater than t. So, all items which have not failed till time t then the proportion of those which continue to work in the interval t t plus delta t so that is represented by z t. So, this is you know interpretation of what I defined here z t as f t upon 1 minus f t. So, this was the conditional probability so life time is more than t and therefore, this is so therefore, z t is the rate of failure so that makes sense. Now, we could we could define z t given the pdf of t. So, the given the pdf of t that means, the f determined z t z uniquely the failure rate the converse is also true.  So, let us see that so the theorem is that if t the time to failure is a continuous random variable with pdf f's and if f 0 is 0 where f is the cdf of t sorry where capital F is the cdf of t then f can be expressed in terms of the failure rate z t as follows. So, then f t can be written as z t into e raise to minus integral 0 to t of z as z s. So, that means, once I know z then through this function I can compute my pdf. So, if suppose you are you somehow know the failure rate you know empirically or somewhere then you can sort of compute the pdf also of t and of course, this makes sense what are we saying that f 0 is 0 implies that r 0 is what 1. So, that means, certainly the function this is we are not going to when the time is 0 then your system is not going to fail it will take some requires some time you start the function the system working or the component is working then only after little lapse of time there is a possibility that the system may fail or something. So, the reliability will be 1 at 0 time and so this is not you know this is a reasonable assumption that m 0 is 0 because you are talking of reliability and the reliability comes only when the system starts functioning. So, some time has to lapse before you can say that the component has failed. So, with this condition now let us start computing f from given z from the given failure rate. So, let us see r t is equal to 1 minus f t differentiate both sides that will give you r prime t as so the derivative of f t is the cumulative density form is the pdf. So, this is minus f t.  So, for f t you are going to write r prime t. So, this is minus r prime t upon r t. So, f t is minus r prime t and therefore, if you integrate this from 0 to t this is of the kind 0 to t r prime s because that is what you have here. So, this is 0 to t z s d s and this will be. So, now you have this integrand of the kind where you have numerator as the derivative of the denominator and so immediately you know that this is the integral of this is minus l n minus sign is here. So, l n of r s log of r s from 0 to t and now here you see this that means this will be. So, if you write it out this will be minus l n r t plus l n r 0. This is what this integral will be, but then since f 0 is 0 r 0 is 1 and log of l n of 1 is 0. So, therefore, there is no contribution from here and you have minus l n r t. So, since f 0 is 0 therefore, r 0 is 1 and so from here z t is this. So, I should write therefore, r t I wrote down this way and this is just integrated 0 to t. So, r t is. So, this is l n r and this is l n r t. So, you have the equation that z t. So, what have we obtained? Now, let that be there. So, the long equation has become long that is why. So, what we obtained is 0 to t.  So, from here we are saying that this implies that r t is so l n. So, e raise to remember when we write l n it means to the base e. So, this will be e raise to minus 0 to t z s d s and now you have it from there see from this equation our original definition because you want to compute. So, I should have finished it here.  So, therefore, f t is r t into z t and r t we have just computed as this. So, therefore, f t is z t into e raise to minus integral 0 to t z s d s. This is what our result was we wanted to show this. And so, given your failure rate z I can compute the pdf of the life length random variable t uniquely. So, there is an interesting relationship between the reliability function r t and the mean time of failure. So, expected t would be the mean time to failure. And so, I want to show you that. So, this is the theorem it says that. So, the t is the random variable and r is the corresponding reliability function. So, I want to show you that e t the expected mean time expected value of t is nothing but the integral 0 to infinity r t d t. So, in other words if you have this then you can integrate this function and also compute e t. There is nothing much great about it we use the same concept that we have. So, remember your definition of r t is the probability t greater than t. So, integral 0 to infinity r t d t will be integral 0 to infinity probability t greater than t d t. Now, this was also I think I gave you this as an exercise in one of the earlier exercises when we were defining expected value of a random variable. But let me now just spend time and show you why this will be true. So, t greater than t if you are integrating now this I can write as integral t to infinity of f s d s probably t greater than t this is what we wrote down just now. So, it is t to infinity f s d s and then 0 to infinity. Now, let us integrate by parts. So, I will treat you know this one as a first function and this is a second function. So, integral of the first function would be simply t and so we want to have this t into integral t infinity f s d s from 0 to infinity plus why will it be plus because when you differentiate this. So, integral of the first into the derivative of the first second and the integral of the whole. So, when you want to differentiate this you see the lower limit is a function of t. So, it will be as it is when you do the you know the first integral the integral of the first function into the second function minus it is a minus sign. But since this is the limit is a function of t the lower limit is a function of t. So, there will be another minus sign. So, and the derivative of this will be 1. So, then f t so plus. So, therefore the sign will become plus and this will be 0 to infinity t f t d t. So, if you apply integration by parts to this treating this as the first function and this whole thing as the second function then you can write this. Now, you can immediately see that the limit at the 0 point. So, this whole thing has to be integrated has to be computed between 0 and infinity. So, at 0 this is 0 and this will be 0 to infinity f s d s which is equal to 1 because f is the p d f and the variable t varies from 0 to infinity. So, this integral is equal to 1. So, this is 0 and now here this is little complicated, but we can see that the limit here s t goes to infinity. So, you see here s t goes to infinity this part becomes 0 and this is going to infinity, but it can be shown that the product here the limit of this product will go to 0. So, once that happens then that integral reduces to simply 0 to infinity r t d t which is I mean it reduces to simply this which is t f t d t from 0 to infinity and this is your p t and so you have this relationship. So, either way you can use it I mean if you know this then you can say that this integral is equal to this or if you know r then you can by integrating this you can compute the expected value of the random variable t. So, now it is we want to study various failure laws that means we want to find out the different p d f s which will be suitable for different situations where we want to study and of course we will keep it very simple here not going to complicated results, but just look at various distribution some of the distributions and we will show why they are appropriate for modeling certain situations for reliability. So, after defining your reliability function and your failure rate we are going to show how important tools they are to you know study these failure models that we will be discussing. So, these are the two basic tools that we need and continuously we will be making use of them. Now, the questions that arise the first question of course then we will ask what underlying failure laws are reasonable to assume that is what should be the appropriate form of the p d f of t you want to know and of course people have you know computed data I mean collected data and then try to fit these various probability laws which are normal exponential and so on. So, that is what we want to say that some of the tested p d f s we are going to look at and tested by tested we mean that you know you try to you have the data you know system is going on and then you compile the failure times and so on of the components and then you try to fit curve and these the ones that we discussed now have been very well tested and you know found suitable for the some particular data that we are going to talk about right. So, when there is a varying effect on the component just as we said that you know beam under heavy load. So, slowly gradually there is a varying effect and then it breaks down. So, for such situations where the varying effect is the one which is the cause of the failure then normal failure law is considered to be appropriate. Consider in the sense that again it has been tested and by fitting the data by fitting you know having the particular kind of data which is you know which is for components failing under the varying effect and then you know finding out that yes normal failure law or the p d f normal p d f seems to give the quite accurate results. So, now therefore, we want to and there are many situations where the varying effect is the prominent reason for the failure of the or the breakdown of the component or the system. Now, when you look at the normal law. So, because the normal law is such that you know if mean is the mean expected value. So, mu is yeah. So, I am looking at the normal law where which is mu sigma square. So, mean is mu expected value is mu and variance is sigma square then this as the bell shape the normal. So, we have already studied I mean in this course I do not have to spend time on describing the normal curve to you. And we know that if you take the area between mu minus 2 sigma and mu plus 2 sigma then area under this these 2 is 0.9572. And if you go up to 3 sigma mu minus 3 sigma mu plus 3 sigma then of course, very little areas left out it is almost I think 0.99 something the area within these 2 limits. And you also see that for t equal to mu this point is the mean as well as the mode that means the maximum failure will occur at around the time t equal to mu. But, since our variable t is takes only non negative values therefore, we will consider the normal distribution that is only the portion from 0 to infinity and not from minus infinity to infinity. So, this normal failure law implies that most of the failures occur around t equal to mu which is the expected value and number of failures decrease as t minus mu decreases in absolute value on either side. So, the number of failures will decrease and the probability goes down and so for example, if you take normal failures law means that 95.72 percent failures take place for t satisfying this mod t minus mu less than mu. So, that means, if your t is in this area then so that will be from 0 to infinity only this portion. So, we do not have to worry about the yeah. So, whatever the mean the expected value the maximum failures will occur around this time. Now, if you look at r t the reliability function then the reliability function yeah. So, r t is equal to 1 minus probability capital T less than or equal to small t right because this is r t is equal to probability t greater than t which can be written as this. And now here you can write this probability for in terms of the standardized normal variate which we have been doing all along in this course. So, this would be equal to 1 minus probability t minus mu divided by the standard deviation. So, this is less than or equal to t minus mu by sigma right. And so this becomes 1 minus phi t minus mu by sigma which is equal to 0.9. Well that I was just considering the value. So, this is the function functional form for your reliability function. And if you plot it here on the t axis then it will be something like this. So, at 0 t equal to 0 your probability t less than or equal to 0 is 0 right because t has takes only non-negative values. So, this probability is 0 at small t equal to 0. So, for this is equal to 1. So, at 0 your value of r t is 1 and when you take r mu then this will be t less than or equal to mu. Now, since t is normally distributed we know that area this area that means this whole area is equal to 0.5 right half the area is on this side and half the area it is a symmetric curve. So, therefore this will be 1 minus 0.5 which is 0.5. So, therefore for mu equal to so this is at mu t equal to mu the value of r t is equal to 0.5. So, this is the kind of curve and then it goes to as t goes to infinity this goes to 0. So, the reliability function decreases with time. Now, so I was saying that see what you can say from here is this is your reliability function. If you want a high value for the reliability function then obviously. So, that means you want this whole thing to be high which that is what I was saying here. So, suppose this is equal to 0.9 and this implies that this must be small and if for this to be small you can again tell by the graph that t must be away from mu this is the whole idea right. Because as we said that maximum failures will occur around t equal to mu and as you get away from mu the values become smaller. So, if you want this whole thing if you want high reliability then your value of t must be removed from mu right. So, for example, if this is 0.9 then this implies that your phi of t minus mu by sigma should be 0.1. This you bring here then 1 minus 0.9 would be 0.1 and so that will make it make t minus mu by sigma equal to minus.   So, it will be somewhere here for the standard normal thing. So, it will be somewhere here point because you want only area 0.1 up from up to this point. So, it will be very small right. So, this is minus 1.2 and so t comes out to be minus 1.2 times sigma plus mu. So, that much removed from mu your value of t is if you want reliability of the order of 0.9. So, take another example now here suppose the failure rate the time life length life time of any component is normally distributed with mean mu and variance 100. So, the standard deviation is 10. Suppose this is this and you are told that the reliability for the 100 hours is 0.99. So, r of 100 is 0.99 you have to find the value of mu that is the expected value of t you have to find. So, since we know the functional form for r t that means again 0.99 is 1 minus phi of. So, we standardized the normal this variate t which is 100 minus mu upon 10 standard deviation right. So, this is phi 100 minus mu by 10. So, that gives you that phi of 100 minus mu by 10 is 0.01. So, again we look up the standard tables corresponding to the area 0.01 this value the value of z is equal to minus 2.33. So, the tables so the see the smaller this becomes the further away you go from the mean value that is what we are saying. So, this implies that mu is see here you will multiply this with this and then. So, it will become 23.3 and mu comes to this side this gets added to 100. So, this will be then 123.3 hours. So, the mu that means the mean is here and so you see this is removed from the mean this is 123.3 hours. So, at 100 hours if you are asking for reliability 0.99 then your mu is this. So, this is the whole idea that you if you have if you if your data or your experience with the system that you are working with is that the normal distribution is appropriate for studying the failure rates then. So, here of course you should also look at what your z t will be. So, if you want to compute which may not be a very. So, for example, your z t we said is f t upon r t. So, which will be 1 upon root 2 pi sigma or let me just so this will be equal to your f t is 1 upon root 2 pi sigma e raise to minus 1 by 2 sigma square x minus mu whole square divided by 1 minus phi of t minus mu by sigma. So, something like this this is your failure rate. So, if you want to compute z you will get this complicated expression, but it seems that here your reliability function is the one which is more useful and has a simple form. Because all you have to do is to for a fixed value for a given value of t mu and sigma if given then you just have to look up the normal tables and compute the reliability of the system at any given time t. Failure law I said to be applicable we want this because obviously, the time to failure cannot be less than 0 with only when this apparatus or the instrument starts functioning then you talk about its failure time and so on. So, time to failure. So, therefore, since this is less than or equal to 0 and normally our the normal distribution extends from minus infinity to infinity, but what we are saying here is that the most of the curve should lie to the right of 0. So, that means here yes the curve should be like this. So, very small area is to the left of 0. So, most of it lies to the right of 0 then the computations would be fine. So, this is very important. So, that means this probability t less than or equal to 0 should be essentially 0 negligible very small that is what we want to say. Now, another way to handle the situation could be that I consider the truncated normal distribution. That means you truncate when you may have your normal distribution this and then you truncated this portion and so that means then you would consider, but then since it has to be a pdf. So, then you will have to so that is what I am trying to say that you know truncated normal distribution. So, if you consider the truncated this normal distribution truncated to the left of t 0 then the pdf would be this, but that is not depicting the actual situation because by this what we are doing is since I want to call this a pdf. So, this integral and of course, this is 0 for x less than 0. So, this is from 0 to infinity. So, what we are saying is that this will be from 0 to infinity this will integrate to 1, but this is not what I want because I want the normal failure law, but it should be such that the most of the curve lies to the right of 0 of t equal to 0. So, that is the meaning and therefore, this of course, this will complicate your computations also, but besides that it will not give you the desired results. So, therefore, the truncated normal distribution is not to be considered. It is simply that keeping this in mind we have to make sure that you know most of the curve lies to the right of 0. So, therefore, when we compute the probabilities they would be approximately alright for and that as I said that the normal failure law is for the aging where the aging is prominent. . So, now we will study we look at the other failure laws which have again been tested for certain different situations and have proved to show good results. So, this will be exponential distribution and available distribution and some others. So, let us look at the exponential failure law. Now, of course, obvious way to define the exponential failure law would be by defining the pdf. So, we say that the pdf of t is alpha e raise to minus alpha t where t is positive takes positive values and then alpha is also some positive constant and then we can obtain r t and z t, but that does not really have that dramatic effect as when you say that the law we say that the failure rate that is z t is a constant is equal to alpha.  So, alpha is your failure rate. So, this is constant and immediate consequence of this is because remember we said that we can given z we can uniquely determine the pdf and also given the pdf we can uniquely determine the function z the failure rate. So, here you see the definition was that f t would be z t e raise to minus integral 0 to t of z s f s. So, here z is a constant. So, therefore, this is alpha into d s integral this leads to t. So, t alpha and here z t is alpha again. So, this is alpha e raise to minus alpha t for all t non negative. So, therefore, this is your so immediately you compute the pdf of t and the converse is also immediate because if you are given that f t is alpha e raise to minus alpha t then this we have already done this computation, but anyway let us just go through it again.  This is probability greater than capital t greater than small t and so it will be e raise to minus alpha t and so it comes down to alpha. So, this is the constant. So, your z t the failure rate is constant. So, immediately we can write down this theorem that and so if I remember correctly we had not done this part that means given the failure rate when I had talked about the exponential when we would we had just introduced the exponential distribution. I had defined the hazard function or the failure rate, but I did not at that time discuss this part that given z t you can obtain your p d f uniquely.  So, immediately we have the theorem that let t the time to failure be a continuous random variable assuming all non-negative values then t has an exponential distribution if and only if it has constant failure rate. So, this is now neat way to present the whole thing that is they can be no other p d f which satisfies the condition that the corresponding failure rate is a constant. So, if a constant failure rate would always be exponential p d f and constant failure rate implies that it is time independent. So, no matter that is the failure does not change with time the failure rate does not change with time. So, no matter therefore, this will be appropriate for situations where there is no bearing effect. So, that means no matter how long the component has been working it does not matter it has no bearing on the failure of the component it will only be some external. So, maybe I will come out with in the next lecture I will try to show you some more you know ways of describing the situations where these different failure laws can be appropriate. So, essentially now try to think of these situations where the failure is not because of the bearing effect at least not because of some kind of stress or load, but it is. So, therefore, as we try to say that if you take a fuse then fuse can be working fine for a long time and then suddenly it fails. So, it is not because may be because of high current or something high current has come and then the fuse burns out otherwise it may continue for a long time. So, therefore, such situations would be very appropriately modeled by the exponential failure law and one can you know now that you read about this you can yourself you know try to think of components or systems where the failures are not because of the bearing effect or this kind of some kind of load or stress, but it is a different kind of failure. And therefore, this can be modeled by the exponential law and you can see that how effectively it will give you the parameters that you require for you know predicting things about the model.


My name is Laura, I'm 28 and I'm from Newcastle.  My ex is Marcel, I'm here on X and the Beach to win back my man. Me and Marcel have literally been on and off for two years now, I'm sick of it. Mainly because he doesn't want to give his attention to one girl and he's a player. One thing I always argue about, girls in social media, following girls, liking girls' pictures, I don't understand it, you've got me. What kind of ex am I?  The best three things about me is we bum the boobs and we ban that it sends a lad mental.  Describe myself in three words, like no other.   Carry on.  So I went the extreme in Messages eBay account, obviously I've got blocks on that as well. The most embarrassing thing I've ever done when I've been drunk is probably get half naked in a club. When I've had a drink I don't know what it is, like my clothes just seem to come off. My ideal date would be a candlelit dinner on the beach, followed by loads of wicked sex. Three sexy secrets about me is I love kissing girls on the night out. I love it, I love naked massages and I love when a guy bites my neck when he kisses us, I love it. My most memorable sex story would be being bent over the balcony in Vegas. I didn't want I was enjoying more, the views on the sex. I came in X on the beach because I actually want Marcel back. I know he's fucked us over in the past, but I actually mean the world he is. So now it's literally now or nothing, he needs to grow up and start being a man.


In this video, I'm going to show you how to get your review link. That way you could send it to people so they could give you reviews to your Google business profile. So the first thing you want to do is you want to make sure you go to the address bar and you want to type in google.com. From there, you're going to go up to the upper right hand corner and it's either going to say up here sign in or it's going to have a circle with either your picture or your initial in it. You're going to hover your mouse over that picture and make sure that whatever email is in this area right here was the one that you used to start up your Google business profile.    You're going to click on it and then right here you can either email it to them. You can send it via WhatsApp, Facebook or right here you can just copy your link by clicking on this little copy button and then it says right here review link copied. Okay, so this will be the link that you use to send the people. That way they give you a Google review. So basically whenever they click on that review link, it's going to take them directly to the area where they give the reviews.