A very good evening to you and thank you for joining us on Y254. My name is Patricia Murioki and tonight we're talking about overcoming the challenges of mentorship. We know that when we talk about mentorship, it's something that every person probably desires to have such guidance in their life so that they're able to know when to make certain decisions and why they are making those decisions. And mentorship is a guidance provided by a mentor, especially an experienced person in a company or educational institution or any other aspect of life. Mentorship are key drivers of success. These personal connections lead to opportunities and promotions that are crucial for career development. Today we choose to focus on the challenges faced through this process and try to find solutions to address the loopholes that are there. To help us talk about this topic tonight, we have Sara Muni, who is a life coach and Gideon Makumi is a vice president youth mentorship foundation, talked to us across our social media platforms. That is at Y254 channel you can also reach me at Patricia Murioki. How are you people? You fine? Yes, we are. We're doing well. You're well? Thank you. It's warm in here. It is good since the weather outside is really not the best. When we talk about mentorship, most of the times people talk about the impact of mentorship. Most of the times we talk about how has that journey been for you? What are some of the things that you've been able to get from that relationship that you've had? But there are these other things that people really don't talk about. And for me to feel that let us address this, it is because I also have experiences that I feel if I was to get certain guidance, I would have done better. And there's also something, some information that lacks in between, which now creates a disconnect between people trying to really identify mentors. And to start our discussion tonight, I'd like to start with you, Sara. When you talk about identifying mentors, how are we supposed to do that? And as I said, should I go and ask, let's say I've seen Gideon, he's in the line of work that I'm doing, and I like his work a bit, I like his values, I like literally how he carries himself around that. Should I go and tell him, Gideon, please mentor me? Should I do that? As I identify mentors in life. Thank you. That's a very important question. It's out of the norm. Yes, but when you identify somebody who you'd like to mentor or somebody who really envisions, I mean, embodies what you want to achieve in your line of career or business, the one thing I'd want to say is if you can or if you in a position get involved in their programs, they must be somewhere possibly running programs or somewhere, because this is what happens. Anybody who is successful, they want to help. They want to reach out, they want to help. So if there's any mechanism or a platform that they mentor people, find out how you can be involved and engaged. The thing is that if you have identified that person, many other people have. So, but many people do that, but they don't really want, they don't want to take part in possibly what they are doing, volunteer in programs or organizations that they run, that's one way. The other thing is possibly if you meet them in a networking event, it's okay, you can let them know what you're doing, what you're passionate about and let them also know that you'd want them to mentor you and which is the best way that you can work towards them mentoring you. This is what I'd like to say at this point. The best mentorship is mentorship that is paid for. Mentorship should not be for free. People don't appreciate, they don't appreciate. This is what happens. I'll find a mentor or somebody who I'd want to mentor and then possibly because they are out there, you know, but we only go when we want to be fixed, when things have happened, things have gone south and then you want to be fixed. It's consultancy, pay for it. If mentorship is a process, subscribe, pay for it, then you'll appreciate it. First of all, because when Sarah said that mentorship, the best mentorship is one that you pay for, you give good. Why? Do you have a different opinion about that? I think people appreciate it. What do you feel when she said that? Well, I agree with her. People don't value free things. Mentorship in itself, it's an investment that one has to make. Nevertheless, on the other hand, I also think it depends with who you're approaching and why and even the background. I understand there are those levels, mentorship, and especially for someone like us, if I needed a mentor, it makes sense if I went and invested in that. But on the other hand, we have that young man, say Korogosho, someone in high school. We may not ask them to pay for the mentorship. So I think it all depends with who is your audience, who is that person seeking mentorship. Are they in that position? Because for example, in my case, I started being mentored from high school. That time I wouldn't have afforded mentorship. But today, where I am, gladly, I'll be able to go and pay my... If I found someone and there's something they have, which I need, most of them out here, you're paying for them. To even be in those sessions, you're paying for them. So I think it depends with the level at which a person is seeking that mentorship. OK. So yes and no. OK. Because I also kind of like have some been... I think differently when it comes to saying that people should pay for like the best is on that has been paid for. And when I was doing research for this topic, I came across a mentor who said that like they were giving a talk and she said that the best mentorship for them is where you also have to realize as a mentor, you also have to bring in... At some point there has to be sponsorship. In terms of you're mentoring this person and when you get to hear of an opportunity, you're finding ways like how can this person probably improving on a certain skill? What are your thoughts on that and how can mentors?  There are people who are like that. What advice do you have for such mentors? Yes. I think as a mentor, your role is to really help somebody be able to up-level where they are, to expose them to opportunities. And the thing is, even for you, it's a win for you when you see this person growing. It's a win for you because you can be able to, when you look back and say, oh, I've been able to help one or two people this far, you feel achieved and happy and fulfilled as a person. So I think that's really the role. So any opportunities... And this is what happens to anybody who is growing or when you reach somewhere in your career, you find very many opportunities around you. They don't all belong to you. They belong to people who are in your space. They belong to people, possibly who you're mentoring your mentees. So that's their approach. And so what really depends on, what it depends on is also how passionate is this mentee? Yes, because there's also, I've spoken of the aspect of paying for mentorship, structured mentorship, which actually you pay, but also as we're beginning and as he was saying, it's good, your passion is what really takes you there. How passionate are you? And also, how available are you? How mentable are you? Because you can only also mentor somebody to the level they're willing to submit to you. So how mentable are you as well? So, I mean, that's the thing when it comes to mentorship. It's looking for opportunities here and there where you can be able to help people, assist people, but also you need to show passion. You need to show interest. You need to push. You need to be present. For mentorship, you have to be present. Yeah, so if somebody is always looking for you, if you're my mentor, for example, and I'm the only one, and I'm the one who, if you're my mentor and you're the one looking for me all the time, all the time there's this opportunity, all the time there's this opportunity, all the time I'll feel like I'm also pushing, you'll feel like you're also pushing me too much and you know, you start. So because I'm the one who is in need, I'm the one to keep coming to, coming to, because there are many people who are also looking for you. So it's up to me to really show the interest and then also whichever opportunities you have as the mentor, you can throw them around. Okay. Yes. Let us to talk about the value of mentorship. Gideon, there is someone out there watching us tonight and they have done their best. They have shown passion and they have literally done everything that probably Sarah has talked about in terms of how you get to identify a mentor and they're not, they're not lucky. They're still out there doing things all by themselves and they've sat down and told themselves, I'm gonna do this by myself, I will learn from myself because I have done my best in looking for this person but I cannot find them. What is the value of mentorship? Now when it's coming, when you have that one-on-one person who's gonna reach out, who's gonna call, when they see you doing things the wrong and they're like, Patricia, I think you need to up your game. You need to go back to the drawing board. What's the, what value does mentorship bring in? Thank you, Patricia. What I think, as far as the value of mentorship is concerned, first, it's very important for anyone seeking mentorship to understand that mentorship is not the only thing that will get you to where your goals are. What mentorship does, it accelerates that journey from where you are to where you want to go because what happens is that your mentor can only do so much. I think 80% is you.  Actually, mentorship is a journey where someone is holding your hand to help you get there but this person may not always be there. Sometimes it is even through an email. You told ABCD, other times, and the best is when someone shares their experiences. So I think for one to get that value, you have to do more than just the face value of it where you are looking at myself and I'm looking at Patricia as the person who will get me to become who I want to become. Let's take mentorship as a place where I'm taking someone as a role model but I'm not taking, it is not their responsibility to make me succeed. It is my responsibility to pick lessons from them which will help me succeed. So it ends at the point of you can do this. Actually, how I look at it is a mentor gives you suggestions and like a coach, a coach will give you instructions. ABCD, a mentor will give you suggestions that if you did this, you're likely to get there. If you avoided this, you're likely to achieve this. So you have to, you can choose whether you pick the lesson or not. So at the point you're getting frustrated, you're saying now I want to do it on my own, probably there's something you're not doing right. But if you follow the suggestions you're getting from your mentor, you stand a chance of getting where you're going faster. Okay. Sarah, before we get to talk about, you get to tell us the difference between a coach and a mentor. This is some, I put this out on my social media and this is what one person said. The problem for me is a lack of mentors. Mentors who really work the journey with you. They feel that's the problem. Do you feel we lack mentors that we're living in an era whereby there are people willing to be mentored but we don't have mentors who are really willing to work that journey with you? I think mentorship these days in the 21st century is a big world. And like I was saying, anyone who is successful out there, they want to help. And if you find somebody who's really successful, they are very mean, they don't want to help, they are not successful. So I think it's a matter of you positioning yourself and exposing yourself to maybe networking opportunities because I can assure you whether it's in the STEM, in science and engineering or in whichever area that you are in, there's somebody who has gone ahead of you and made it, yes. So mentors are there. It's about positioning. It's about you recognizing what do I really want first of all, because not everybody can mentor you. In which area do you need mentorship first of all? Who are people playing in that space? Make it your business to know your business and to know your industry. Who are the people making it in that industry? Who are the dons in that industry? Make it your business to know that. And also, where do they go? Which clubs do they go to? Are they part of like lottery clubs? Are they part of, make it your business to know where they go. And these days it's very simple. You just need to go to somebody's Facebook page to know maybe what event they will be in. Or I mean you can always find that Twitter, go to LinkedIn. These days you can even speak to Bill Gates on LinkedIn. They are there. They are there personally. Not even just they are technical teams. They are usually there. You can follow somebody. You can know what they are working on and be part of what they are doing. So that's mentors are there. That's I think the first thing I want to assure anybody who thinks there are no mentors around them. Mentors are there. Position yourself. Identify what exactly you need and also reach out. Be mentorable. Be mentorable. And like you are saying, in one of the challenges you find in mentors, I don't know of somebody who's always there. You know, it's not really the business of your mentor to really follow you every time they are there. They are making sure that oh, you know, as if it's a responsibility really for you to really succeed. Well, they are responsible. We are part of the responsible because when they accept they want to assist you but it's you to really push and be present and be, you know, really show that passion. You know, then you be able to get there. Because like you were saying, they can only do so much. You know, the rest is really up to you. Yeah, the rest is really up to you. So what now is the difference between a coach and a mentor so that people don't get these two mixed up? Yes, I'm a coach, you know. But I'm also a mentor, you know. I think let me give this analogy. A coach is somebody you want to travel.  You want to travel. You want to go to, let's say, to Uganda, possibly some exposure. You have never been out of the country as a young person. A coach will tell you exactly what you need to do together. They will not go with you. They will tell you, okay, if you want to go there two ways. You can fly or you can go by road or you can walk. So if you walk, it will take you this number of hours. You will follow this route, you will get there. That's one, that's higher. Then they'll also tell you. You can also use, you can go to Simba Quartz. You can go to Guardian, those buses. You will pay this much. And by 10 hours, you'll be in Kampala. They'll also tell you, if you go, and if you do that, you'll actually get there.  Just board a plane, you pay this much and in about an hour, you'll be in Kampala. If you do that, you will get there.  They'll tell you, okay, we have this route, we can go there, we have this another one. They will actually go with you. They are tour guides. Coaches are travel agents. Let me say that. Actually they let you know, you got it out for yourself. But you will get there. But mentors, they are tour guides.  It's like this. Watch it to cool it, watch it to cool it. Yes, they'll go with you. I think that's the best analogy I can use. Okay, and I really like it. And I hope that people really get to differentiate the two. Yes, I know like a mentor, like I know most people watch football. I mean, it's all soccer stories. When we have the coaches, yeah, like Mourinho, I mean, Jose Mourinho, do they play? No, they don't. They don't play, but they're able to stand somewhere and look at, okay, who's one of these players? I'm not a football fan, I'm sorry. So I cannot help. Who's one of these players? Can you believe us? So they're able to look at a player. I think you can best play number nine. You can best play striker. They can be able to stand at a vantage point and tell you, okay, these are your strengths. Maximize on them. These are your weaknesses. You need to improve here.   So they're just instructing you. They're able to stand somewhere. But then there's another person who can actually tell you, okay, let me go to the field with you and show you this is how you do the, is this a goal kick or the corner kick? What? Yeah, that's it. I hope those two analogies have helped you get the difference between a coach and a better. You need more. Okay, okay. So I think that we need to address something where people feel that is not people looking for mentors. There is this organization. You want to be mentored by the CEO who comes in the office probably twice a week. And you have your head of department there who can be willing to mentor you. But because your aiming, your aim is up there. There's no problem with aiming. But I think how can we now come and create a balance in being very realistic, even the people that we want are probably to mentor us. Because I feel probably we might not find mentors because of even our approach that we have. What do you think, Gidya? I think first it has to start with the objective. Why do you need a mentor? What are you looking for in that mentor? Because you can have different types of people mentoring you. You can have someone mentoring you in career. You can have another one mentoring you in business. You can have another one mentoring you in life issues. So I think between your CEO and your HOD, what is my need? If my need is probably to get to know how I can get, raise my business through to where my CEO is, then I think my CEO becomes a better choice. But if my business is to know how do I make my leadership skills better? How do I manage even the, maybe the other HOD, how do I manage maybe another level of employment on my team? Then I think a HOD becomes better. Because that is what they are doing directly. So the need should guide their approach. What you're looking for should be the one informing you that Sarah is the one that I need. But if probably it's not that coaching I need, I need someone who will help me know how is the media world. Then Patricia becomes the best person. And I like what Sarah has said.  I think we need to realize that whereas I need this person to work with me as a mentor, I also need to know that they have other things that they are doing. And if I know my CEO even at office, I only see her once in a week, for example, then that means she's so busy, I may not get all the time that I think I need to grow. But my HOD, they are there with me every day. So which is a prudent choice? Getting the person that I think will be available. Because going back to the question you had asked, sometimes we blame our mentors that they're not there. But in essence, they cannot be there always. So I think you have to be wise enough. And Sarah said it right, know where they are. Just know their schedule in this place. If my mentor is the kind that is not even in the country all along, then I'll blame them. Yet they are doing what they're supposed to do. But I can get another person who is another option who will also guide me in the same. So mentors are there in plenty, but we have to know what we want for us to choose the approach that we're going to use to get that person to mentor us here. Okay, and today, because you said we're talking about challenges, these are the things that people don't talk about. I was talking to a friend today who felt like was when I told her like what I'm going to be talking about tonight, and she told me, I feel that women struggle in identifying mentors more than men. What do you think, Sarah? Wow, that has not been the case for me. I think because you're driven by passion and people can see it, let me tell you, it attracts, passion attracts. Passion is attractive first of all. So how passionate are you about your goals, about what you want to achieve here? So maybe that could be a study that has been done, but in my experience, because I've also mentored women. You know, I've also mentored women. Also that women, not many women are willing to extend the mentorship and the guidance to other women. Okay, wow, wow, wow, yeah. So I'm also a beneficiary of mentorship from women, yes. And in my experience, I haven't seen a case where I approach somebody and, you know, they outrightly refused or anything. I haven't seen that. Maybe widely, well, it's there. There are ladies who don't like mentoring other ladies, but like I said, if you're really successful in an area and you don't want to mentor, you're not really successful, yeah. So for me, in my experience, I think I have seen women who have been very, very willing to assist, who have programs. You know, also, there are people who are up there, they've done some things very well, but also they don't have structures, really like a structure where they can get people together.  Getting this person becomes a bit hard, you know? And unless you really, really follow, unless you really, really look for them, they are not, you find like, they are not there. Yeah, you find like they are not there. But I don't want to sit here and say that I've found women to not to be, you know, they don't like me. I can't really say that, I will not be fair for me because I've benefited. And I've seen many other who have benefited from other ladies. Possibly Gideon has a different view, yeah. I think, I'm of different opinion. I think it's all about, it's about the personality of the person. And I've also seen women even wanting to do more than men. Ironically, starting with my boss. I mean, our boss will be the best mentor you ever find. And I believe in that value of, a mentor is happier when they see you succeed even more than they have. Than when they see you fail or when they're the only one shining. And if I don't want anyone to go beyond where I am, I think I'm even limiting myself in the sense that I'll never get to the next level if I can't allow another person to come to where I am. I always remain where I am. So really, I need to allow myself to be useful because someone else was also useful for me to get where I am. So it's only fair to return that and do it to someone else. So women, I think they do it to more than men. It will not be just if we don't talk about this, over sharing. You have a mentor who is guiding you in your career as a journalist. Are you supposed to be going to tell this person, oh, I have this problem. Oh, my village has done. I need this, this. How much should you share with your mentor? Where do we now draw the line? Because I feel some people overstep and their mentor is like, wow, I think this is not becoming too much for me and they didn't start them. So which is very okay and which is very allowed. So before you get to talk about when kind of mentee, let go of a mentor, Sarah. Yes, actually, you know, people go all the way. You know, sometimes the kind of view we have about mentorship is that, you know, mentor should do everything for me to succeed. They should give me money. I can come to his office without money and they are supposed to fix me. Please don't borrow your mentor's money. It's manalive. It's not good at all. Because, you know, and then, you know, it's not bad to share like I had this challenge and all that, but don't look needy. Don't go to them looking needy. Like you need help. I also have to ask if you're looking for sympathy. Don't, no, no, no.  You know, be decent and really just address whatever it is that, if it's assistance in business, just say this is really my need. There's no problem with you saying you have a wedding. Yeah, yeah. There's no problem. But, you know, don't look needy. How much will you contribute for me? Let them make the decision. Let me tell you, mentor, they want the best for you. They want the best way they would do anything possible.  So, but don't look needy, first of all. Yeah, don't. Do not. Yes. Unlimited. Unlimited. Yes. In addition to that, I think it's very important for us to understand that the person I'm going to get as a mentor is not a perfect person. It's not an angel who came from heaven to come and now show me the way. This person has their own needs. They have their own issues. Probably they have even bigger, stressing issues than you do. They are also trying to continue winning whatever section they are. So, sometimes when you go to them, like begging, it's very, very unprofessional. I think what you're supposed to do from the beginning define the objective of our relationship. As we start, this is what I need and let's define how we are going to do, to work around it. Because when you do, people get pushed. Even if I had so much money, sometimes I feel so pushed back when all you do is to come and tell me the problems that you have. If I'm willing to come and assist, or if I ask you, for example, were you able to pay your rent this month and I'm willing to chip in, that's a different story. But in August, I don't have rent. In October, I don't have rent. You push me away. Not because I am not willing to help, but because I feel the objective of our relationship is not being met. Okay. As we wind up, because time is now not on our side, at what point has a mentee? Because it doesn't matter because this person is one who's up here at the other one. They're the only ones who see things the right way and all that. You can also see it some and be like, hey, by the way, it's been three months, there is no impact. This mentorship relationship is not really, it is not impacting me in any way. What point do you say, thank you? And how do we say it in respectful ways? Because we may need them 10 years down the line. Sarah, as we close up, please. And you can also actually outgrow your mentor. Yeah, it's true. But when you find such a situation, you don't go to your mentor and say, okay, thank you for your mentorship now, I'm God. Mentorship is a lifetime process. And even the person who helped you when you were in primary school, maybe they invited you, they guided you in some way and you know for sure your life is where it is because somebody back then helped you. You don't look down on them and say, okay, now they have no value, no. So just maintain that rapport and relationship, but maybe possibly at a distance, you know. Try and check up on them sometimes, you know. But don't just let it, it should not be official like now. I've gotten enough of your mentorship, see you in the next level, see you in the next life. No, no, no, you don't do that. Just maintain a good, I mean, it's wisdom. You know, it's wisdom. And if you find you're actually doing better than your mentor, but you know, don't try to show them or try to share in, to show them that you're sharing whatever, it's apply some wisdom. Just keep contact, keep a rapport with them, but also look for people who can really push you now to where you're going. Yeah, because actually you cannot grow your mentor. Okay. Gideon, I want to give you that second. What is the one thing? I just, not long story, not telling stories. What is the one thing that has helped you really maintain the best of relationship with your mentor? Because I happen to know your mentor and they don't like you have the best relationship. As you wind up. Thank you, Patricia. Special thanks to you. He's my mentor. He has helped me become, he has raised the boy in me to become a man. That says it all. I am a man from Korogo Show. It's now a man doing something better than I would have done if I wasn't having a mentor. So my mentor has really helped me become a better man. Okay. Thank you very much for finding the time to be with us tonight and share your sentiments on this topic. I hope that for people who are watching us, I hope that you've learned all I can tell you is that mentorship is really important. If you find yourself in a place where you have a mentor, do everything that you find these two people talk about. And also if you're at a position to, if you're in a position to extend the mentorship, the wisdom and the knowledge that you have, do not keep all that to yourself. Let us share because at the end of the day we all need each other. Thank you very much. My name is Patricia Muriuki. Do have yourselves a very good night.


I am Srikanth Chitrapati. I have had a good satisfying treatment in Manipal, North Side Hospital, Malaysia. I got admitted to the hospital due to Riga fever in 2018. Due to prevalent wound on the sole of my feet, I was diagnosed with Blood Infection II, which has affected my heart functioning. Dr. Nagesh Cardiology treated me and is treating me. From stage of criticality, I have recovered thanks to Dr. Nagesh for an insightful guidance and treatment. I am almost back to normal. Dr. Nagesh has been prompt with his timings, listens to patients' problems and treats them without much ado. The front office, sisters and the hospital have been responsive. Heart is vital and special to everyone. So cardiologists are more special. On this World Heart Day on 29th September, I wish the heart-carrying doctors and patients the very best, including the nursing team in Manipal Hospital. Thank you.


In the previous lecture, I have shown that how the signed ranks that is the ranks of absolute values or the modulus of x i's can be used to create a test for the ah non parametric location problems. ah Let us consider further the quantities which are called Walsh averages W ij this is defined as the average of 2 of the observations x i and x j. So, this W ij these are called Walsh averages. Then if I consider t plus which I defined as the Wilcoxon-Simland statistics this is actually the number of positive Walsh averages. Let me call it statement number 1. Let us look at a proof of this say suppose I take n is equal to 1 that means, only one observation is there. So, that means, it is only x 1. So, t plus that will be 1 if x 1 is greater than 0 and it is equal to 0 if x 1 is less than 0. And here only one Walsh average is there only one Walsh average W 11 that is equal to x 1. So, if it is positive. So, then it is t 1 t plus is equal to 1 and it is negative then it is equal to 0. So, 1 is satisfied for n is equal to 1. Suppose this statement 1 is satisfied for n minus 1. Now, we have to add x n there and that means, we have to consider the modulus of x n. So, without our loss of generality we take it to be largest. Suppose it is not largest then we can consider another permutation of that in which it will become the largest. Since, we are assuming that one is satisfied for n minus 1. So, whatever permutation we take in that permutation also it will be true. Therefore, without loss of generality. So, without loss of generality we take modulus of x n to be the largest. So, now let us consider t n plus 1. So, I have put subscript here just to denote that it is based on n observations. So, it is t n minus 1 plus if x n is negative because that will not add to the t plus t plus is the sum of the ranks of the positive one. So, if it is negative then it will not add and if it is plus then since it is I am assuming to be the largest its rank is n. So, that will be added here. Now, what are the new Walsh averages? When I am adding nth observation then the new Walsh averages that will be coming the new Walsh averages obtained after adding x n they are x 1 plus x n by 2 that is W 1 n W 2 n that is equal to x 2 plus x n by 2 and so on. W n minus 1 n that is x n minus 1 plus x n by 2 and W n n that is x n. Now, if x n is less than 0 I have assumed that modulus x n is the largest that means in absolute value it is the largest. So, if this largest absolute value if it is negative then whatever be x 1 x 2 x n minus 1 ultimately they will make it negative. So, W 1 n it will become all of them will become and of course, W n n is negative. So, the number of positive Walsh averages remains the same. On the other hand that is t n minus 1 plus if x n is positive if it is positive and since it is the largest in magnitude therefore, it will make whether it is positive or negative it will make all of them to be positive then W 1 n this is positive and so on W 2 n W n minus 1 n W n n they are all positive. So, the number of positive Walsh averages increases by n that is t n minus 1 plus n. So, thus 1 that is the that is t plus is the number of positive Walsh averages. So, I can call it as a theorem here which I have proved now by using induction by mathematical induction this result is true all the time. Now, based on this let us define the indicator function d i j is equal to 1 if Walsh average is positive it is equal to 0 if Walsh average is negative of course, equal to 0 we do not have to consider because of the assumption of the continuity of the random variables the probability of W i j is equal to 0 will be 0. So, then t plus is the number of positive Walsh averages and that is actually equal to double summation d i j i is equal to 1 2 well i less than or equal to j 1 less than or equal to i less than or equal to j less than or equal to n I can write here. If I consider p as the probability of x i greater than 0 when true median value is theta p 2 is the probability under the true median value theta of x i plus x j being positive. So, I call these values p 1 p 2 then in terms of p 1 and p 2 we can write expectation of t plus that is equal to double summation expectation of d i j 1 less than or equal to i less than or equal to j less than or equal to n that is equal to expectation of d i that means for the ones which are j is equal to i and then those terms for which it is less. So, this is equal to sigma probability of x i greater than 0 under theta and in the second one it is equal to probability of x i plus x j greater than 0 because actually I have defined in terms of directly the value 1 and 0 only for positive and negative therefore, this is simply this. So, it is actually becoming n times p 1 plus n into n minus 1 by 2 p 2. So, under the alternative that means if median is any other value theta then the expectation of t plus will be in terms of this. Similarly, if we look at the variance of this. So, for variance we need the expectation of this square. So, that is expectation of double summation d i j whole square. Now this you can write as expectation of summation d i i plus summation d i j. So, this is i is equal to 1 to n and here i less than j. So, this is equal to now let us expand these terms. So, it is becoming d i i square and here what are the terms that we will be getting see all of the terms will be coming here and then there will be a cross product also. So, we can express it like this the terms for which. So, basically square of all the terms will be coming here because square of this and square of this. So, I can put double summation i less than or equal to j and this I can make i j here. Now cross product terms will be of two types. One is from here and one is from here. In this one you can consider i i and j j kind of terms here. Here you can see that the terms will be i j and may be well first one may be same.   So, these many terms will be coming when I square it this. So, now if I look at expectation. So, expectation here and in each of them it can be applied let us look at this. So, this expectation is equal to n times expectation of say d i i square plus n into n minus 1 by 2 expectation of d i j square plus here of course, i is less than j plus twice n into n minus 1 by 2 expectation of d i i d i k where i is less than k of course, all of them are under the assumption that the median is theta plus twice n into n minus 1 into n minus 2 3 into 2 expectation of d i j d k j this is for i less than j less than k twice n into n minus 1 into n minus 2 into n minus 3 by 4 into 3 into t 2 expectation of d i j d k l here i is less than j k is less than l and i is less than k. So, if you combine all these terms here now some additional probabilities will be coming earlier I defined p 1 and p 2 but now because this one will involve some joint probabilities let me write it here. If I define say p 3 is equal to probability of say x i plus x j greater than 0 as well as x i greater than 0. Similarly, if I define p 4 is equal to probability of x 1 plus x i plus x j greater than 0 x i plus x k greater than 0. So, this term is then becoming n times p 1 plus n into n minus 1 by 2 p 2 plus n into n minus 1 p 3 n into n minus 1 into n minus 2 by 3 p 4 plus n into n minus 1 into n minus 2 into n minus 3 by 12 p 2 square. So, once we have the expectation of t plus square expectation t plus is already there. So, we have the expression for the variance of t plus also. So, that is basically this term minus expectation theta t plus whole square. So, I am not writing the whole expression here it is simply the repetition. So, in case the median value is some theta then also we have been able to derive the probability in the moments etcetera of the t plus here. If you look at the nature of this statistic that we have used here it is defined as the ranks of the positive ones and then u x i. Now, in play. So, these are some functions of x i's or some functions of modulus x i. So, we can consider various choices here and with various choices one can consider the general scoring function and we call it a linear rank statistic. So, general linear rank statistic for a general scoring function. So, in general we consider a 1 less than or equal to a 2 less than or equal to some a n and we define s is equal to sigma of a i u of x i i is equal to 1 to n. So, as examples you can see if we are considering a i is equal to 1 then it is sin rank sin test. So, these are called sin scores. Second example is if a i is equal to i then s is Wilcoxon where. So, these are called then Wilcoxon scores. So, this actually this a i's are called score function. There are some others also like for example, you may choose a i is equal to in terms of the cumulative distribution function of standard normal that is half plus i divided by twice n plus 1. These are called normal scores and then there is another one called Fraser's normal scores where this z i is actually the ith order statistic among modulus of z 1 modulus z 2 modulus z n where z i's are i i d normal 0 1. So, if I consider a random sample from a standard normal distribution and I consider the absolute values then the relative position of modulus z i that is ith order statistics. Then based on that if I define this then it is called Fraser normal scores. Since the null distribution of u x i is known therefore, we can look at the mean variance etcetera of s in the general sense here. So, if I look at say expectation of s that is equal to sigma of a i that is half. So, it is sigma of a i i is equal to 1 to n. So, in all the cases when these are only permutation of numbers 1 to n then this will become simply n into n plus 1 by 2. For example, in the Wilcoxon score it was like this for sin this was 1. So, it was n by 2. So, like that there can be various choices here. If I look at variance of this then it is equal to sigma a square i variance of u x i i is equal to 1 to n that is equal to. So, half minus half square that is 1 by 4. So, it is 1 by 4 sigma of a square i i is equal to 1 to n.  Based on this if I consider the expectation of s etcetera then what I will get u of x i. We have already proved that the distributions of r i plus and x i are independent. So, this becomes expectation of a r i plus into expectation of u x i, but this is half here. So, it is simply becoming half times expectation of a r i plus, but if I summing over all of them then it is simply all the values are coming here that is all and variance of s will be simply 1 by 4 sigma a square i i is equal to 1 to n. So, in general we can prove the following theorem that the distribution of s is symmetric under h naught. So, for a proof let us look at what is the probability that s is equal to minus some s. So, we will prove actually it is symmetric about its mean. So, it is probability of sigma a j u of x i j expectation as we have already calculated. So, it is simply minus s here. Since the distribution of u x i j and 1 minus u x i j is the same because what is u x i j? u x i j takes value 1 with probability half and 0 with probability half when the null hypothesis is true that is when the median is assumed to be 0. If that is so, then if I look at 1 minus u x i j that is also having the same distribution because that is also taking value 0 and 1 only each with probability half. So, in this statement I can replace 1 minus u x i j that is half sigma a i minus s. Now, this term you take to the other side. So, you are getting it is equal to p naught sigma a j u of x i j j is equal to 1 to n is equal to half times sigma a i plus s that is probability of s is equal to expectation s minus plus s. So, the distribution of s is it is symmetric about expectation of if it is not under h naught then the distribution will not be symmetric because then the distribution of u x i j and 1 minus u x i j will not be the same. Here since it is under the null hypothesis so, both the probability of x i j being positive or negative is half. Now, this part you can see this is a general theory because I am not assuming a particular form of s here general I am writing general scores a i is there. We have seen that the asymptotic distribution of the Wilcoxon sign rank statistic the asymptotic distribution of the scientist statistic they are all normal asymptotically. There we were able to do the exact calculation. So, here it is in the terms of a i's if we impose certain condition on this is scores that a i's etcetera then here also we can obtain the asymptotic distribution to be the normal. So, we impose some condition these are called no other's conditions named after a me no other. So, let us define this no other's condition what is the no other's condition the no other's condition is maximum of a j square for 1 less than or equal to j less than or equal to n divided by sigma a square j j is equal to 1 to n this goes to 0 as n tends to infinity. So, this is called no other's condition then we have the following result that is under no other's conditions the distribution of s minus expectation s under h naught divided by square root variance of s this converges to standard normal as n tends to infinity. Now you see here the expression for the general linear rank statistic I have written in terms of summation here. So, if we use this Lyapunov's center limit theorem we can do that thing.  So, let us write that let us write say w i is equal to a i u x i we can also write it as a j u of x i j as we have done in the previous one it does not matter. So, w i is equal to a i under the null distribution it is equal to half and probability that w i is equal to 0 that is also half. So, if I look at the expectation of w i that is a i half and therefore, if I look at the I call it mu i then it is equal to half sigma half a i now let us look at the second one sigma square. So, that will be equal to half half a square i minus 1 by 4 a square i that is equal to 1 by 4 a square i. So, sigma square then that is becoming equal to 1 by 4 sigma half a square i i is equal to 1 to n we also need the third central moment here. So, the third central moment here will become equal to w i minus a i by 2 cube. So, when it is equal to a i it is simply becoming a i cube by 8 and then you are dividing by 2. So, it is becoming by 16 then when w i is 0 then it is becoming again a i cube by 8 then half. So, a i cube by 16 that is equal to a i cube by 8. So, rho cube is equal to sigma half a cube i 1 by 8 i is equal to 1 to n. Of course, there is one comment here I did not mention about a i's what are the values of a i's a i's are either 1's or 0's in this for example, in the case of in the sign rank it is 1 to n otherwise it is i etcetera. So, in general actually we are taking a i's are positive. So, this term I did not mention earlier what it is required otherwise you have to again put modulus here. So, we have to consider rho by sigma it is more convenient if I take the power 6 here. So, it will become that is 2 to the power 3. So, it is becoming 2 to the power 18 and here you are having 2 square. So, that will become 2 to the power 12. So, some coefficient times. So, some constant times you will get sigma of a cube by whole square divided by sigma a square i whole cube. Now this term we separate out this is less than or equal to in one of them I put maximum here. So, this is less than or equal to maximum of a square j for 1 less than or equal to j less than or equal to n. So, basically what I am doing I am splitting it and in the second term I am writing it as simply sigma a square j whole square and in the denominator I am having sigma a square j whole cube. So, this term gets cancelled out. So, by no other condition this goes to 0 as n tends to infinity. So, s minus expectation s divided by square root of variance of s that is actually s minus expectation s we have already calculated here that is half sigma a i divided by square root 1 by 4 sigma of a square i. This goes to 0 this goes to z as n tends to infinity. So, the asymptotic distribution of the general linear rank statistics are satisfied and actually for the sign test statistic for the Wilcoxon sign rank statistic it is already satisfied. I wrote two more scores that is the normal scores and the Fraser normal scores for that also one can actually check that this will be satisfied. Now, the procedure that I have developed for single sample problem in some cases they can be also extended to two sample problems. For example, if we consider bivariate and we still want to compare the locations of both of them then we can take the differences. Now, based on the differences if you look at the distribution of that and we define this ranks of that differences then this test statistic will again work here. So, let us consider these extensions to various other cases we can also look at some confidence in double procedures etcetera ok. Let x 1 y 1 x 2 y 2 x n y n be a sample from a bivariate population and we want to we want to test say equality of medians theta x and theta y of x and y sample populations ok that is the separate population. That means, my hypothesis testing problem is something like this theta x minus theta y is equal to 0 greater than 0 less than 0 not equal to 0 etcetera. So, here we can consider say d i that is equal to x i minus y i. Now, based on d i we can consider say we will coxson test or sin test etcetera. Another application is to look at the confidence interval we can also construct confidence intervals. Suppose we are considering some other number say u 1 u 2 u n star suppose they are observations and they need not be independent also need not be independent. We can consider say t 1 is equal to number of u's which are greater than say 0, t 2 is the number of u's which are less than 0 then we can take minimum of t 1 t 2. So, based on this we can consider let us call it say t star we can reject h naught if. So, hypothesis is say theta is equal to 0 against theta naught equal to 0. We can reject this if t star is say less than or equal to some c where this should be equal to alpha. Now, this can be determined as we are saying minimum of t 1 t 2 greater than c is equal to 1 minus alpha or we can say t 1 is greater than c t 2 is greater than c is equal to 1 minus alpha and this you can consider as say u of d less than theta naught well less than 0 less than u n star minus d plus 1 is equal to 1 minus alpha.   We can also consider point estimation problem. So, let us consider say z 1 z 2 z n be a random sample from a location parameter distribution f x minus theta and symmetric about theta and let us consider say h of z 1 z 2 z n a test statistic for h naught theta is equal to 0 against say h 1 theta greater than 0 and suppose we reject for large values of h z then this you look at this h satisfies the following conditions. One is that h of z 1 plus a and so on z n plus a is non decreasing in a for each of z 1 z 2 z n. Second is that h of z 1 z 2 z n is has a symmetric distribution about mu under h naught. If we consider say theta star is equal to supremum of those values for which h of z 1 minus theta and so on z n minus theta is greater than mu and theta double star say that is equal to infimum of those values theta for which h of z 1 minus theta and so on z n minus theta is less than mu. If I consider say theta head is equal to theta star plus theta double star by 2 for scientist for example, here h of z 1 z 2 z n is the number of z i's which are positive then h is symmetric about n by 2. So, here theta star will then become equal to supremum of theta sigma of u x i minus theta greater than n by 2 i is equal to 1 to n that will give me theta star is equal to x n plus 1 by 2. If n is odd and similarly theta double star that will become equal to x n plus 1 by 2. So, what we are getting that theta head is equal to x n plus 1 by 2 as the estimator of the median theta. So, basically we are getting a sample median as the estimator of the population median. If n is even then if you calculate these quantities theta lower upper star that will become equal to x n by 2 and theta double star this will become equal to x n by 2 plus 1. So, theta head is then again sample median thus we obtain the sample median as an estimator for the population median. So, this linear rank statistic or this core function that is actually useful in deriving confidence interval for deriving the point estimates it can help us in testing about the equality of the median in a bivariate problem also. So, these are various applications of general linear rank statistics. Then the other problems that come is comparing the medians of two independent samples. So, in that case this directly cannot be used. So, let us consider separately the two sample problems. So, our next topic in this nonparametric method says two sample problems or two sample location problems. So, let us consider say in fact, I have already given the form of U i's and U bracket i's etcetera. So, we will see how these terms are used. So, x 1, x 2, x m be a random sample from a continuous population with cdf say fx and y 1, y 2, y n be an independent random sample from a continuous population with cdf gyy. Suppose this x is so we are already assuming that they are independent and in general we want to test say fx is equal to gx for all x against not equal for some x. So, this is a general problem of equality of the two distributions, but in particular we can consider location equality problems in equality problems, scale equality in equality problems and general alternatives. Let us consider say location problems here. In the location problem we consider h naught as that fx is equal to gx for all x and in h 1 gy is a location shift of f for all x for some theta. So, this is interesting here. I have actually if you consider the standard problems in the normal distribution etcetera, then these problems are directly related to the equality of the location that is the mean etcetera. Here it will become in terms of median you can say. So, we can consider if theta is greater than 0 then we are basically saying it is equivalent to saying that median of f is smaller than median of g. If theta is less than 0 then median of f is larger than the median of g. So, the hypothesis testing problem is this is equivalent to testing h naught theta is equal to 0 against h 1 either theta greater than 0 or theta less than 0 or theta naught equal to 0. These are the alternatives actually. So, as you can see that it has come down to the original type of problem here. Now, we will introduce a test-test statistic it is called one Whitney Wilcoxon test. When the null hypothesis is true then basically we are saying the two distributions are same and then this x 1, x 2, x m and y 1, y 2, y n this can be actually considered as one sample and if it is one sample then all the arrangements of this x 1, x 2, x m, y 1, y 2, y n among the numbers 1, 2, m plus n they will be equally likely. So, if I consider the probability of any arrangement of m excess among m plus n observations then it will be 1 by m plus n c m or 1 by m plus n c n. So, we utilize this concept here basically we consider counting of how many y j's are less than x i's how many y j's are greater than x i's etcetera actually that will directly give us a hint of this testing problem. You can see that in the case of parametric inference we look at the means of the observations. Since here if I look at the means of the observations etcetera the distribution will be extremely complicated because we do not know actually what is the form of f and what is the form of g. Therefore, we have to do or we can we have to actually work with the numbers only that is the ranks or the how many of them are positive negative, how many of them are greater than the other one because the probabilities can be calculated in terms of capital f and capital g, but we cannot calculate expectations and other quantities if we do not have the basically we cannot find out the distribution of the sums of the observations or the means of the observations. So, that is the difference between actually the methods of the parametric inference and the non parametric inference. In the parametric inference we directly go down to the sufficient statistics we check whether it is complete or not and then we base our inferences on that. In the case of non parametric that is not possible and therefore, we work with the order statistics we work with the signs of the things we work with the ranks. So, under H naught we observe that under H naught any arrangement of m x's and n y's are equally likely. So, probability of any arrangement is 1 by m plus n c m which is also equal to 1 by m plus c. Let us consider say define d i j that is equal to 1 if y j is less than x i and it is equal to 0 if y j is greater than x i. So, this is defined for all i is equal to 1 to m and j is equal to 1 to n and then we define u is equal to double summation d i j for i is equal to 1 to m and j is equal to 1 to n. This u it is actually known as Munn-Whitney Wilcoxson u statistic it was given in 1947. Now what are the possibilities here it could happen that all the y j's are greater than all x i's in that case value of u will be 0. If you have all the y j's less than all of x i's then all the d i j's will be 1 and therefore this value will become equal to m n. So, the values of u this will vary from 0 to m n and therefore it will test the departure from the equality of the medium. So, for example if more of the y j's are less than x i's then that means d i j is higher value that means the median of y's is less than the median of x's and that is equivalent to saying that median of g is smaller than the median of this one then it is actually equivalent to theta less than 0. Similarly if this is smaller then we are getting theta less than 0 that means if d i u is smaller then more of y j's are larger than the x i's that means median of y's may be tending to become higher than the median of this. If that is so then you will get theta greater than 0. So, this hypothesis will be true and similarly for either very large or very small you will have theta not equal to 0. So, all the 3 cases will be actually satisfied here. So, this statistic u tests the departure from theta is equal to 0. If u is large then median of y's will be larger than median of g will be larger than median of f that is theta is less than 0. If u is small then median of g is g is smaller than median of f that is theta is greater than 0. So, we can consider the following test that is reject H naught at level alpha if u is less than or equal to c alpha this is for alternative H 1. u is greater than or equal to c 1 minus alpha this is for alternative H 2 and for the third one for u less than or equal to c alpha by 2 or u greater than or equal to c 1 minus alpha by 2 this is for alternative H 3 and this c beta is the largest u such that probability of u less than or equal to u is less than or equal to beta or c 1 minus beta is the smallest u such that probability of u less than or equal to u is greater than 1 minus beta I think they should be greater than or equal to. In the next lecture we will discuss the null distribution of u's how it is obtained the mean and variance under the general hypothesis. There is a related one which is called Wilcoxon a statistic for the two we will define the general rank statistic for the two sample problem we will look at the asymptotic distributions of that. So, these are various things that I will be taking up in the next lecture.


What's something really cringy that brands do on social that give you the ick? Constantly saying bestie.  When I started Babe, it was like no drinks head of voice, but now every drink is just like, yeah, it's like, I'm you, do you love euphoria? Like we love euphoria and I'm like, I don't need you to like connect with me on like whether or not I'm like a Maddie or a Cassie. Gotcha, which one are you? A Cassie. I knew it. The quintessential like hello, fellow youths meme, like you can tell somebody was like, oh I bet I can trend with the thing without actually understanding what the thing means. When brands do like a viral trend and it's like three months after the trend's done and then they still try to do it. They hop on trends or memes that don't make sense for their brand. And then it's this awkward moment of like, okay, I like this brand, but they're posting something cringy, do I engage with it? I think it's like when they're just trying to enter TikTok, but they just haven't really thought of a strategy yet and they're just tossing up some content without much, you know, real thought to it. I think that just drives me nuts. Yeah, my feelings are like personally hurt by that answer.  In a f***ing sense.  I'm gonna f*** Tumblr. I think there's a place in town for that and it's never social media. What the f***? I think there's a lot of great creative, fun inventive ways to connect with consumers without getting quite so thirsty. The sex jokes, it's gross. It's gross, I'm sorry. I don't wanna see it. I don't wanna hear it. I don't need to watch two mascots humping each other. I'm sorry. I'm fine being on the wrong side of history with this one. If you see a brand deal and it just looks such an ad and it's somebody talking like a robot, I think I don't like that. Ads that aren't innovative, that aren't engaging. Just a static paid ad on Facebook just makes me feel like blah, bored, onto the next. You could tell that an ad is very scripted. That's how I know to stop working with certain brands because I feel like if you wanna work with a certain content creator, it's because you like what they're putting out there. Using a celebrity or a really well-known influencer for their brand when you know that they've never used their product. Asking for participation is tough. Like, quote, retweet, follow for shares. Honestly, I think it's just running cut and paste creative across different socials. As a creative strategist at Reddit, that we're always trying to do is just really make sure you're coming authentically to the communities and the people you wanna speak to. Only celebrating a certain affinity group for a month. So Pride Month is coming up and it's just like, oh now we're rainbow flag or Black History Month or AAPI Heritage Month shout out it's our month. So it's just like, that makes me cringe. It's like, what are you doing for the rest of the year? What are you doing for the rest of the year? Like, we wanna know.


Alhamdulillah, Allah Subh'anaHu wa Ta'ala has truly blessed us with an opportunity to do great, great, great immense good for our souls. According to all appearances and sometimes appearances can be deceptive, there are many challenging days ahead for the Muslim community here in North America. Which means what? Which means that Allah Subh'anaHu wa Ta'ala has given us an opportunity to be patient. Allah Ta'ala has given us an opportunity to be patient and thereby to do great, great, great immense good for our souls. Nothing in our religion has been rewarded patients with the exception of fasting which in the view of many is synonymous with patients. Waste'eenu bas-sabri wa s-salat. Many of the exegents mentioned commenting on this and a couple similar verses, ayi bas-siyami wa s-salat. Waste'eenu bas-sabri wa s-salat ayi bas-siyami wa s-salat. Seek the help of Allah, patience and prayer, that is to say with fasting and prayer. Ramadan shah-ru s-salat. Ramadan is the month of patience. In any case, why do we say there is no reward except that equals or equates the reward for patience? The Prophets of Allah ﷺ remind us, al-haste'eenu bi-ashli an-thaliha. Al-haste'eenu bi-ashli an-thaliha ila s-sab'eenu bi-adha ila ad'abun kathira. The good things that you do, your prayer, your recitation of Qur'an, your awrad, your umrah, your hanj, whatever you are commanding the good, or bidding the wrong, your sadhaka, your assisting people, you're visiting the city, etc. All of these deeds are multiplied ten times over, seven hundred times over, many times over and beyond that, but they have a numerical limit. As we mentioned specifically with the exception of fasting in terms of our deeds directly. All of the deeds that you do, al-haste'eenu bi-ashli an-thaliha. Wa qawallahu a'az-zawajal illa s-siyyama fa innu liwa an-nacb. So Allah exempts from that multiplication of the d's the fast. Except fasting, that is mine, I will reward the fasting person. The ulama they say that the reason fasting is exempted is because it embodies patience and the reward for patience has no miracle limit. As Allah subhanahu wa ta'ala reminds us in the Quran إِنَّ مَا يُوَفَّ الصَّابِهُنَ أَجْرَهُمْ بِغَيْلِهِسَا إِنَّ مَا يُوَفَّ الصَّابِهُنَ أَجْرَهُمْ بِغَيْلِهِسَا The patient ones will be given their reward with no miracle limit. بِغَيْلِهِسَا So patience is rewarded with no miracle limit. In many instances in the Quran we find the reward of patience mentioned after the mention of tremendous difficulty and struggle. For example Allah ta'ala mentioned وَلَنَبْلُوَنَّكُمْ بِشَيْئِمْ مِنَ الْخَوْرِ وَالْجُوَةِ وَالْنَقْصِمْ مِنَ الْأَمْوَالْ وَالْأَنْفُسْ وَالْثَانَرَاتِ وَالْبَشْرِ الصَّابِيرِ وَبَشْرَ الصَّابِيرِ Then surely you will be tested. لَنَبْلُوَنَّكُمْ Inferently وَالْتَقْدِعُ وَالْلَّهِ وَالْلَّهِ لَنَبْلُوَنَّكُمْ بِشَيْئِمْ مِنَ الْخَوْرِ وَالْجُوَةِ وَالْنَقْصِمْ مِنَ الْأَمْوَالْهِ وَالْأَنْفُسْ وَالْثَانَرَاتِ وَالْبَشْرِ الصَّابِيرِ By Allah you will surely be tested. With something of fear. So it won't be overwhelmed. Some people are apprehensive now. But they go about their daily business. Do not overwhelm. بِشَيْئِمْ مِنَ الْخَوْرِ وَالْجُوَةِ And something of hunger. Some Muslims are tested with starvation right now. Places like Syria or other places. But that's not the overwhelming, the dominant condition of the 1.7 billion Muslims on the face of this earth. Most Muslims are well fed. And the great cuisines of the world. Most of them are Muslims. The Turkish, the Iranian, the Afghani. Look at the restaurants in the area. The North African, the Cuscus, Shawirna, Doner Tiba. It's all Muslim. Mantu, Bulani, Ash, Qabuli. It's all Muslim. Muslims eat well, generally. بِشَيْئِمْ مِنَ الْخَوْرِ وَالْجُوَةِ وَالْنَقْسِمْ مِنَ الْأَمْوَاتِ وَالْأَنْفُسْ وَالْتَمْرَةِ And a loss of wealth and lives and fruits وَالْبَشْرِ الصَّابِيرِ Give glad tidings to those who patiently persevere. In the face of that loss. In the face of those tests. Give glad tidings to those who patiently persevere. وَبَشْرِ الصَّابِيرِ Allah Ta'ala mentions elsewhere. And words that are incredibly prescient in terms of our current situation. وَأَذَنْ كَثِيرًا وَأَنْ تَصْبِرُ وَتَتَّهُوْ فَإِنَّ ذَا لِكَ مِنْ عَزْمِ الْأُمُورَ That surely you will be tested in your wealth and in your persons. And you will hear from some of those giving the scripture before you, not all of them, because some of them are friendly, wonderful people. And from some of the idolaters. And then, كثيرًا, much abuse.  Then know this is only something Allah Subhanahu wa Ta'ala has informed us about for over 1400 years ago. That surely directly addressing the community of the Prophet ﷺ but it's part of it. Everyone after, they're acting. And then, كثيرًا, وَإِنْ تَصْبِرُوا But if you patiently persevere in the face of that abuse, in the face of that foul language, وَتَتَّحُونَ And you remain mindful of Allah Subhanahu wa Ta'ala and mindful of your duty to Allah Subhanahu wa Ta'ala فَإِنَّ ذَا الْكَمِنْ عَسْلِنْ قُمُورَ Then that is a demonstration of resolve in your affair. And that places you or adorns you or allows one to adorn himself or herself with one of the characteristics of the greatest of the messengers and prophets to walk upon this earth. They're called Ulul Azim. Ulul Azim. فَإِنَّ ذَا الْكَمِنْ عَسْلِنْ قُمُورَ So this is a characteristic befitting Noah. And a characteristic befitting Abraham and a characteristic befitting Moses and a characteristic befitting Jesus and a characteristic befitting Muhammad.  Fasbeer. Fasbeer كما صاورة أقول العزني من الرسول How shall we persevere our Muhammad? Fasbeer يا محمد That's not mentioned but the address is directly to the Prophet ﷺ. Fasbeer. Patiently endure كما صاورة أقول العزني من الرسول As those great messengers who preceded you endured and persevered and were patient وَلَا تَسْعَجْلَّهُنْ You're going to be hasty and dismissing your people and riding off your people and turning your back to your people and responding to hatred with hatred towards your people or bigotry in the face of bigotry as Kipling says and if you can be hated not yet give way to hating if you can keep your head when all of them are losing theirs and blaming it on you very appropriate for our day and time if you can trust yourself when all men doubt you yet make allowance for their doubting too if being hated not give way to hatred these are the messages that we need to take the heart brothers and sisters because these are the times and it's in times like this where the opportunity to manifest prophetic characteristic is called for to have the prophet, the patience brother that the prophets displayed to have the good opinion of people that the prophets displayed what is the opinion of the prophet towards the people of thought when they sallallahu alaihi wa sallam when they stoned him when they humiliated him when they turned the imbeciles and the children of the city and unleashed them against him in a humiliating terror of abuse perhaps there will arise from the progeny those who worship Almighty God when the angels invited him to call upon them to bring the great mountains down upon his enemies he refused to do so when at the height of the battle of Uhud a very desperate situation where defeat was snatched victory rather was snatched away and then a very psychologically traumatizing defeat was inflicted upon the Muslims and in the thick of the fray when so many good people are falling the Hamza, Musa al-Nayr and others and the prophet sallallahu alaihi wa sallam he's desperately wiping his blood from the injuries on his mouth on his cheek rather and his mouth and they ask him why he said if the blood of the prophet hits the ground during the battle then God will bring his wrath down upon his enemies and then they asked him to pray against them and he said sallallahu alaihi wa sallam and he said I wasn't sent to curse people I wasn't sent to damn people I wasn't sent to invoke the wrath of God down upon people I was sent as a mercy sallallahu alaihi wa sallam I was sent as a mercy so brothers and sisters patiently persevere despite the trials and the tribulation no matter how difficult they might seem to be no matter how daunting they might appear persevere forge on and note that you have a righteous cause that you embody the very best of human behavior characteristic if that characteristic reflects the prophetic virtues that we've been taught our prophet sallallahu alaihi wa sallam he said in explaining his mission and there are other explanations but this was one he emphasized I've been sent as a teacher I've been sent as a teacher and so in the face of ignorance what better thing can we do than to teach people in the face of ignorance what better thing can we do than teach people ignorance only exists in the absence of truth darkness only exists in the absence of light جاء الحق وزحق الباقي إِنَّ الباقي لَكَانَ زَهُقَى truth comes in falsehood parishes falsehood rains especially falsehood concerning the Muslims in our community because we have not brought the light of truth to our neighbors to our co-workers to our fellow citizens we have a calling brothers and sisters and it doesn't involve something glamorous or something that requires focus to groups to determine what to do just be yourself and tell people who you are just be yourself and share your religion with people be yourself and explain to people how this or that balancing relating to Islam is not true invite people to your homes invite people to the library invite people to the mosque to the masjid so that you have an opportunity to explain yourself for yourself and not to have yourself misrepresented by someone else so patiently persevere I have been the eminent the eminent movement the affair of the believer is amazing the affair of the believer is amazing his affair is good his affair is good his affair is good his affair is good and that is for no one except the believer in the past he was a good believer if some good defiles him if some good defiles her he or she they think that they think that they thank God for his graces and that's best for them every good you enjoy brothers and sisters the freedom you enjoy the food that you enjoy the clothing that you enjoy the shelter that you enjoy the safety and security that you enjoy despite all the tension in the air no one is fearing right now that some lunatic will run in here and perpetrate some ghastly crime against us we sit here in safety and security that's a great blessing thank God for that blessing thank Almighty God for that blessing let them worship the Lord of this house and an aspect of our worship is shukr is gratitude let them worship the Lord of this house the one who has fed them and driven hunger away from them and made them secure for prayer brothers and sisters we should be absorbed in our worship as gratitude to our Lord for feeding us and driving hunger away from us and for blessing us with safety and security in our homes and our places of worship as we go toward back and forth in the streets conducting our business and there are exceptional incidents that happen here and there but they're statistically insignificant 4, 5 or 6 incidents 7, 8, 10 incidents in a country of 319 million people since the election people are tense and uptight that the elections have unleashed all of these these nasty and putrid forces that we thought we overcome by and large but despite that have any Muslims in this country been shocked since the election killed or abused there are incidents but how many people have died in car accidents since the election of the president pilaf how many people have died in the strangest of ways that we don't even take note of no Muslims have perished no Muslims have perished no Muslims have perished no Muslims have perished we should thank Allah for that as opposed to working everyone up into a frenzy that leaves them vulnerable to their faith being eroded we should strengthen people's faith and work to reinforce their faith so that if things do happen they will have the strength and the fortitude the word of thought to forge life and to be patient and to trust in Allah to trust in Almighty God that His promise is true that His promise is true and that this world is just a test it's not the end of things one of the terrible terrible conditions or situations we see affecting many of our young people is that they're affected by an intellectual paradigm that's rooted in Neo-Marx's atheism that there's nothing beyond this world therefore all justice has to be secured now all good has to has to accrue to a person now and that if justice is not forthcoming if good does not accrue to the person then one has to engage in desperate needs to ensure that it happens because this is all there is if you're a Marxist this is all there is this world if you're an atheist this is all there is this world but if you're a believer we believe that there's something beyond this world we believe there's something greater than this world we believe that this world is so insignificant it doesn't even it's significant doesn't even equate the wing of a mosquito this is the world as we mentioned on several occasions where you don't know this is the world on several occasions where you to take the 100 years if you had a good long life and only 100 healthy years and not 60 healthy years and then 40 torturous years that you wish you never experienced that it was all over at 60 but 100 healthy good years what would that look like if we placed it on a continuum that started with the creation of the heavens and earth and extended into eternity because paradise or hell are realities that will extend until eternity with no end what would that 100 years look like you couldn't even begin to measure it but there are those who would jeopardize eternal bliss for some passing fleeting gratification in this world this is not how a believer sees it a believer understands there's no perfect justice in this world a believer understands perfect justice is with that a believer understands that there is no unrequited suffering in the world that suffering will be rewarded patience in the face of suffering will be rewarded this is what a believer understands and believes to the very depths of his or her of her soul may Allah give us patience Iman al-Shaki he mentioned that one chapter in the Quran only was revealed it would have sufficed the people in that insana la fi khus by the witness of time where the passing ages or the declining day where the humanity is lost the only exception except those who believe and they do righteous deeds and they counsel each other with truth and they counsel each other with patience so brothers and sisters be patient and understand that your patience as we mentioned unlimited reward and understand these are days where patience is required we say this in conclusion as we reminded by our Prophet sallallahu alayhi wa sallam in the end of time there will be days that are called which are called days of patience and one who holds on to their religion during that time is like one holding a smoldering ember a red hot ember like those charcoal briquettes when you barbecue in the summer and you just put the lighter fluid on and they're red and glowing imagine holding one of those and you just put the lighter fluid on and they're red and glowing imagine holding one of those in your hand that's how difficult it will be to hold on to your religion and we our scholars teach us that the reward for an act is commensurate to the difficulty of the act so if it's that difficult to hold on to your religion what is the reward what can actually and the reward for one who continues to practice who continues to act who continues to hold on is like the reward of 50 men men whom al-minna ya Rasulallah 50 from them or 50 from us 50 from you 50 companions the reward of the one who continues to hold on will be like the reward of 50 companions radiya allahu alaikum the brothers and sisters hold on be patient forge on continue to do the good things that you do work to improve your religion and to refine your religion work to grow closer to the Quran as each passing breath draws you closer to your death study the life of the Prophet sallallahu alayhi wa sallam i understand the tremendous challenges he was faced with and how he patiently persevere through them i say in qaudi haider sallallahu alayhi wa sallam As-salatu wa sallam assalamu alayhi wa sallam sallam's salatu wa sallam assalam e-salaam insalam sallam as-salatu wa sallam As-salatu wa sallam as-salatu wa sallam In the face of all of the difficulties and challenges are popular in the world, Subh'Allah was able to smile. The sadness was in his heart and not on his face.  It's a struggle, but it's a struggle punctuated by many opportunities for celebration. It's a struggle punctuated by many opportunities for leisure. May Allah subhanahu wa ta'ala bless us to take advantage of those opportunities with families, with friends, to share a meal, to share the outdoors, to hike and to ski and to do other things that bring happiness into our hearts and that rejuvenate us so that we're better prepared to go back into the struggle. And that's what life is, it's a struggle punctuated by moments of leisure and celebration and then those who rejuvenate us and we invigorate us and we jump back into the fray with greater resolve and greater energy and then we celebrate again. May Allah bless us to be able to celebrate life. May Allah bless us to be able to celebrate life. May Allah bless us to be able to celebrate life. May Allah bless us to be able to celebrate life. May Allah bless us to celebrate life.