Hello everyone. I'm Brian Reel and I am an Assistant Professor of Information and Library Science at Southern Connecticut State University. I'm one of several co-organizers for this conference. The others are Oliver Geichen of the University of Maryland, Martin Johnson of the University of North Carolina, Chapel Hill, and Audrey Amadon and Heidi Holmstrom of the National Archives and Records Administration. We've been helped along the way by additional staff members of the National Archives, some of whom are taking a visible part in the conference, and others who have remained behind the scenes. This conference would not have been possible without the tremendous institutional support we have received from both the National Archives and the University of Maryland. Several of us who are involved in this conference are members of the Association of Moving Image Archivists, also known as AMIA, and a major part of that organization's conferences is its archival screening night. After all, if you spend a few days talking about how to do the work of motion picture archiving and preservation, it's nice to actually see some of the archives' holdings. While this served as a model for us, AMIA's archival screening night is usually something of a grab bag from different archives, while for this evening, we are primarily focused on the holdings of the National Archives. Audrey, Heidi and I picked a few things just because we thought they were cool, but for the most part, we let our conference participants offer feedback and guide our selection process. Heidi will speak more on that in a moment. We are showing extended clips for the most part, to allow our program to have a bit more variety. We are extremely grateful for Dennis Doros and Amy Heller of Milestone Film & Video for hosting this screening for us through their Vimeo account, and especially for their steadfast work in supporting film and media archivists over the years. As you watch these films, please remember that they are available because of the work done by archivists. This is a team effort that goes beyond just film and media archivists. Without the work of archivists to arrange, describe, and provide access to paper records and other documents, we would not have the information needed to contextualize and understand many of the films we are showing this evening, and that our presenters will discuss during the conference. And with that, I will turn things over to Heidi. Thank you, Brian. My name is Heidi Holmstrom, and I am a film preservationist in the National Archives' Motion Picture Preservation Lab. Films made by the U.S. government were intended to document, educate, and persuade, and we will be showing you selections from many films tonight to illustrate these different types. I worked with Brian and Audrey Amidon, also from the Motion Picture Preservation Lab, to choose films that help illustrate the themes of the Films of State Conference. We will see films about the U.S. government's relationship to the land, the activities of the military, and the government's communications with people both at home and abroad.  We are going to open the screening with Land of the Lofty Mountains, a silent park service film that has been given a wonderful new score by pianist Andrew Simpson. And with that, let's roll the film. Save valuable energy dollars. Apply weather stripping, storm windows, and storm doors. Then caulk all cracks and small holes. Energy-saving home improvements can eventually pay for themselves in lowered fuel bills. You will also help save our energy sources. If you don't have the cash, you may qualify for a HUD-insured Title I home improvement loan. Write HUD Energy Saver Washington, D.C. 20410. It was early morning in Georgia. Long before daybreak in a lone house at the edge of the forest, a boy lay awake with excitement, for this was to be an important day in his life. He had hardly slept the night before, but not his brother, Harry. In all fairness, you couldn't blame Harry. For him, it was just another day of work. But for the boy, it was the first day of his vacation from school, and he was going to make the most of it. His father was still asleep, and he took care not to wake him. In the kitchen, his mother was making breakfast, and it would soon be ready. Though the boy and his family lived on a small farm, they were people of the forest. His father and brother made their living with the stroke of the axe and the pull of the saw. And today, for the first time, the boy was to work at their side in the forest. Often say, you're as old as you feel. Today, the boy felt like a man, and he was ready and anxious to prove it. It felt good to the boy having wonderful people for a family. His mother made me a gentle woman who gave loving care to her family. His father, Louis, a kind man, who was as wise as he was strong. And his brother, Harry, who worked hard and said little. Together, they were the Hunter family. For over 80 years, the Hunter family has owned this farm. The boy's grandfather and his father before him cleared this land and planted cotton and tobacco. But ever since James's father was old enough to lift an axe, he had been a woodsman, cutting and hauling logs. His tools were the simple tools of the forest, the axe, and the two handle saw. I can remember when this was clear. Looks like some dirty birds were here. Looks like somebody dumped oil into the stream. Someone through paper cuts me to it too. You can't build a pop can. Why do people do this with you? Well, Greg, they just don't think. They forget to be careful. But that's how we can help. Now, if we see a mess, help clean it up. But most important, don't make a mess in the first place. Come on, kids, let's get busy. Help would be spread the word.   Don't pollute.  In the snow or on the sand, don't keep America looking, Greg. Oh, help would be spread the word.   Don't pollute.  In the snow or on the sand, don't keep America looking, Greg. Hello, boys and girls. I have a special message for you from the President of the United States. Let me read it to you. I salute the boys and girls who are buying United States savings stamps and bonds through the Treasury School Savings Program. They're learning the lessons of practical citizenship and of why his money management, and they're giving important support to the cause of freedom and the men who fight for us in Vietnam. That message is on this wallet-sized U.S. Savings Bonds pledge card, which you'll get in school as soon as you begin to buy U.S. savings stamps. Let's get started today. What do you say? Today, you can safely say that a tactical map is also an Army film distribution map, stretching for countless miles in every direction. But this is only the beginning. From here on, the films and equipment must be moved to the interior, must be moved by whatever modes of transportation are available, and those that can be improvised. Naturally, much is contingent on the risk and terrain, but it can be said that wherever supplies are moved, by what means they are moved, so the films are carried right up to the threshold of battle. In the skies over the battle-scarred southwest Pacific area, film containers are part of the cargo en route from New Caledonia to a strategic island outpost. Below is Bougainville. Similar landings are made throughout the Solomon Islands and surrounding areas, where our hard-fighting troops are making it hot for the Japs. The welcome passengers begin the last leg of their journey, moving right up with a mail bag. Letters from home and movies tonight at the Bougainville Roxy. The films are greeted like long-lost friends. Weary but eager warriors converge on their little theater as the word races through camp. A brief lull means that some of the men can see the new show, while others keep up the jungle watch. The names of these island battlegrounds are familiar to all who follow the war in the Pacific. Yet how many know that men star for entertainment are carving their own makeshift theaters out of a tangled wilderness. These scenes and all that follow were photographed by combat camera crews. This is the real McCoy, spot coverage that breeds realism into all that has been written about the average GI and his craving for motion pictures. Wire reels for seats, coconut logs for seats in a palm grove selected for added atmosphere to even line up all the empty gas barrels in sight. Anything that can be sat on, ingenuity born of necessity, and their arrangement makes good sense right up to the placement of the projection booth. Sometimes rear echelons can go in for fancier and more permanent structures. This is the best in the area. But fancier otherwise the same results are produced. Countless thousands of war miles, millions of troops, heterogeneous in other respects, yet maintaining a mutual interest in screen entertainment. This is the story of a young man who discovered his true calling in the war-torn skies of Europe. Wilbur Bloom of Oxford, Ohio volunteered for the US Army Air Corps in 1943. After completing flight school, he was assigned as a bomber-deer on the B-25 medium bomber. In March 1944, he arrived in recently liberated Corsica, home of the 340th bomber group, and was soon flying his first combat missions. One of the most remarkable things about the Second World War was the degree to which it was documented on film. Many Hollywood directors and cameramen had volunteered for service. In addition, hundreds of young men with an aptitude for photography and cinema were identified and pulled together to form combat camera units. They operated in every theater of the war. Lieutenant Bloom, a camera enthusiast, was transferred to the newly formed 9th Combat Camera Unit in June 1944. He got his hands on IMO and Mitchell cameras, and began making movies. That summer, the commanding officer of the 340th assigned him to produce a short documentary called Training During Combat. The objective was to show how continued training in forward combat zones contributed to the group's success. I was keen to see this example of my father's early work. I also had reason to believe that the film contained unseen wartime footage of another young bomber-deer, Joseph Heller, who gained fame two decades later as the author of Catch-22. In 2014, my search led me to NARA. To my surprise, they rapidly located nine reels of unedited footage from training during combat that was shot by Lieutenant Bloom. The combined running time of this footage is nearly 73 minutes. Of this, over eight minutes contained scenes showing Joseph Heller in uniform. It is unclear whether the film was ever completed. What you see here is an edit that the NARA team made based loosely on the script. A C-47 has just pulled up on the landing strip. An eager replacement crew piles out of the plane. Young Joseph Heller, playing a new bomber-deer, is the second man down the steps. Excited and a little cocky, the guys throw their baggage into an open truck and drive off to the operations building. The new crew gape at veteran airmen returning from a mission. The next moment, they encounter the group commander who welcomes them. A wacky grin breaks across Heller's face as he shakes the commander's hand. The men are eager for action, but they can save their bravado for later. The Colonel has recommended a regimen of lectures and training sessions. The gunners work out on trainers armed with dummy machine guns that squirt pressurized water at moving model planes. This one simulates combat for a ball turret gunner. The pilot and bomber-deer practice their coordination for bomb runs, crawling over a cement floor aboard a special training device. Here you can see Joe Heller operating the top-secret Norden bomb site. Between missions, the pilot sharpens his skills on the link trainer. Inside this dark gyrating capsule, he flies on instruments alone. This gunner is getting more practice on the tailgun trainer so he can shoot enemies attacking from the rear, emblazoned on the device is the squadron emblem. In case of a hydraulic system failure, crews can lower the landing gear using a manual crank. In this scene, enlisted men and officers use a REC B-25 as a demonstration model. Concentric steel hoops define fire zones for top-side gunners. These are some of the finest shots of young Joseph Heller in the film. They depict the new bomber-deer's visit to the squadron navigator for a few pointers. It was an important relationship because the bomber-deer had to do most of his own navigation during the bomb run. For targets that were especially difficult to identify on the final approach, models were built to study the features of the terrain. The time has come for the new men to put their skills to the test. All the crews listen intently as officers conduct the briefing. The new crew huddles for a final confirmation of the plan before loading their bombs. They're ready to go. The pilot fires up the engines and taxis to the end of the runway, lining up with the other ships from the squadron. To the roar of its twin engines, the plane picks up speed. Take off! Once airborne, the pilot joins three other B-25s in a box formation. In the plexiglass nose, the bomber-deer looks out the window and confirms the target. Bombs away! Today is just a final test. The target, an uninhabited rock in the sea. The bombers peel off for home. Their crews confident and well-prepared for combat. The brief and exciting year with the 9th Combat Camera Unit was the springboard for Wilbur Bloom's career. Returning to civilian life, he enrolled in the graduate program at the University of Southern California Cinema Department. Upon graduation, he joined the faculty at USC Cinema where he taught for 10 years. His first major triumph came in 1956, when his short film, The Face of Lincoln, was awarded an Oscar by the Academy of Motion Picture Arts and Sciences. Bloom produced films for the U.S. Air Force during the 1960s, working out of Lookout Mountain Air Force Station, a secret production facility in the Hollywood Hills. Projects included a series of people-to-people films for the Pacific Command. In 1973, he joined the USIA as production manager of the Motion Picture and TV service. He enjoyed the frequent collaboration with overseas filmmakers, actors, and writers. In the final phase of his government career, Wilbur T. Bloom was director of Motion Picture and Television Policy at the Department of State. He retired from the Foreign Service in 1981. In his later years, he taught public policy and communication at the United States International University in San Diego. He had seen a lot of the world, influenced students, filmmakers, and public diplomacy, and made many, many friends.  Sit down, Lucas. Thank you, sir. You know, Lucas, I've been wondering about you. During the week that you've been here, I've noticed that, unlike the other men, you don't talk in our group sessions. What is it to talk about, sir? Lots. You hear the other men getting quite a few things off that chest. You should be able to see that they feel better by so doing. What ship were you on, Lucas? The Montandan, sir. The Montandan was sunk, wasn't she? Yes, sir. Last May, south and into now in a high sea, torpedo at. And you were a fireman? I am, sir. Certainly. And it's a tough job being a fireman. Always below decks, you never see what goes on. That's why I'm fed up. Nobody gets it. Nobody. Maybe not. And yet there may be some of us, even among those of us who haven't been there, who do understand. What do you, sir, know about what it feels like to be a fireman?  You've got to be there to know. You've got to feel that goddamn heat. On the Montandan there was always 128 degrees below decks. 128 degrees of sweat and more sweat. No place to go or to move to. Those guys topside have it soft. They can breathe air, move around, see the enemy. Hell, we don't know whether the next minute will bring a bomb or whether there's a torpedo coming for us right now. What was your job in the engine room? I was striking for water, Tender. I was the lines feeding water to the boilers. That's why I couldn't move. I had to stay with those goddamn valves. The guys topside and take it out on the enemy. They can shoot a gun. All I could do was wish I could twist a valve, but I couldn't because I'd wreck the boiler.  Goddamn it, look at me. Stitch isn't me, doctor. How did you feel, Lucas, when you knew you were safe in the water? How did I feel? Yes.  Anybody would have been. No, Lucas, not everybody would have been. That's something you've got to face. Furthermore, you didn't really find relief, did you? I said I was glad to get out of that hole. Perhaps for a while. But I doubt it for long. How about it, Lucas? How about it? I got the feeling I let my buddies down. That's it, Lucas. And that's something you've gotten away to feel proud of. You were in a tight, tense situation. And quite naturally, you were afraid. You and every other man on that ship. Your buddies in the engine room, the gunners topside, you were all afraid. Because that's what happens to men in a battle. You were no different from any other man on that ship. Only most of them accepted their fear. You fought against yours. If I only could have been topside, if I could only have moved around. It would have made no difference.  You wanted to get out of the engine room. That's why you felt relieved when you were in the water. Even though you'd been blown from the engine room, as far as you were concerned, you were the state.  As a result, you feel guilty. Yes, sir. That's a feeling that you have to face and conquer. And the only way you can do that is to understand that the real cause of your being here is your normal fear and time of battle. Fear which you didn't learn to handle properly. That you're continuously short tempered, even mean. With your handshake, you'll have a burning sensation in the pit of your stomach. All stemmed from this cause. Now, in order to start getting well, you have to realize this. And in realizing it, remember that fear and the thoughts that it makes you think at the time are normal. Nothing to be ashamed of. Shared by all of the other men who were with you on the mountain. As well as by the men on all ships. A ticking bomb means trouble for Batman and Robin. Holy, breaking and entering. It's Batgirl. Quick, Batgirl. Untie us before it's too late. It's already too late. I've worked for you a long time and I paid less than Robin. Same job, same employer means equal pay for men and women. No time for jokes, Batgirl. It's no joke. It's the federal equal pay law. Holy act of Congress! If you're not getting equal pay, contact the Wage and Hour Division, U.S. Department of Labor. As we approach the 21st century, there is much to learn about our world and ourselves. This learning occurs best in a climate of equal opportunity. In that sunny climate, human intelligence, trust and total commitment can prosper. We become the winning team. For purposes of testing equipment and we no longer had a need for that, we gave that up about three years ago. But that is where the water immersion facility will be built if you will be. I would like to go into space for a couple of reasons. The space program meets my particular academic needs. It gives me something that's intellectually challenging, also physically challenging, but much more important, I think, that man needs something to dream about. We've explored our world fairly thoroughly. I realize that there are oceans remaining in that three quarters of our world, but there's really just two frontiers left, the ocean and space, and I'd like to be part of that effort. I certainly feel that women are here to stay as part of the space program. This time, all the women selected were selected as mission specialists. I certainly feel that in future selections with women training as pilots that there will be women selected as pilots. I think we're here to stay. Who is to say who will succeed or fail in any task we earthlings undertake? For is there really any difference between the minds of males and females? The women of NASA don't think so, and neither does NASA. For it is generally agreed that differences in performance occur when there is a difference in opportunity to learn and to gain experience. When I was picked about a year or so ago to be a backup payload specialist on a dress rehearsal of a space shuttle flight, I was afraid at that time because I thought, well, maybe I really can't do it. But as it turned out, I was picked because of the investigators who had submitted experiments, just as it'll be for an actual flight. The payload specialists, the scientists, astronauts are chosen because maybe there's some particular characteristic of their own experiments that would make them themselves be the best person to conduct that experiment and also because their background, their educational background is varied enough to be able to adequately carry out other people's experiments on board. And as we went through the simulation I found out that I could learn what I had to learn, that I was doing just fine. As we approach the 21st century, drifting through the universe at almost a thousand miles per minute, increasingly we are coming to realize that equal opportunity, intelligence, excellence, and teamwork, rather than race, creed, color, or sex, are the keys to success in space travel. Whether we happen to be aboard a space shuttle or on board our mothership. Alright. He gets all over your pants and shirt. I don't think that I will talk. I don't talk all by himself. Don't you know? I will. It's no everything. Closer, because I've got something to show you. Now, what's it worth to me? What's it worth? It's worth 20. Now listen, folks. What you got to show us? She's going to show you how he does that. Well, I have a movie to show you, Mr. Home Run King. How do you do that? Now, I started to tell you I've got this movie to show you. That's just great. What's this about? Lottery? Wait, let me go get the dream book. No, not that kind of thing. Social Security number every morning. It keeps me dry all day. Well, the Social Security number I'm talking about won't let you down either, friend. And this is a film about Social Security that I want you to see. And what it can mean to you. Make way for the old folks. They need this more than we do. Come on here just a second. Uh, says... Uh, says this ain't for old people. And listen, if they want to. Security has something for those about. But it also has important benefits for young people, too. Or to your mother. That does it. I'm leaving. Hey, let the owl talk. Just stay with me, folks. This film also has information that's important to know when you're working. Say, that little girl in red in the back, she's awful cute. But how are you going to take care of her if something happens to you? And you can't work. I don't know.  Well, like I said, why don't you listen to this film? Because Social Security has something for everybody. And this film will show you just what I mean. Are you ready? One of the best sounds around was the People Crackers' plant number five marching band and groove society. Hal Hippo blew first sousaphone. And Robert Rabbit hit lead block and spiel. They were really fine days. The band was doing gigs all over the town. And Hal and Robert were kept busy every weekend. During the week, they were kept busy at the world's largest maker of People Crackers, a big favorite of all the animals. But when they weren't working, they always found time for fun. The good times did roll. And the hippos and rabbits enjoyed the good life all the way. One fateful day. It happened. Harry and Robert were working a big Independence Day celebration with all the works. Hal Hippo gone almost a month now. And Robert Rabbit still unable to walk. The doctor still thinks it might be as much as two more years before Rabbit is back to normal health. Mrs. Rabbit is worried because they're using their savings for day-to-day expenses. Then one fateful day. This is where I come in again. Excuse me, folks, you mind if I come in? Uh, Mr. Walrus, the funeral director. And Mr. Raff, the teacher down at the school. Well, they told me about your problems. Mr. Raff was very worried because she hasn't seen the children for some time. Normally people come to us about their benefits. But I think your case is special. I'm from Social Security. But I'm not retiring. Oh, quite right. But Social Security isn't just for retirement. It protects your family at any age. For example, why aren't the children in school? They're all looking for part-time jobs. Because Robert isn't going to be able to work for at least two years. And our savings won't carry us that long. They should still be going to school. Who'd work then? Mrs. Raff and I have the little ones to take care of. And we have to eat and pay that rent. That's why I'm here. Both Hal and Robert had Social Security at the plant, didn't they? Sure, for retirement. Uh, you forget now. I said there are other Social Security benefits. Seven people from Iran who had received the best education from more than 310 people in their studies spent the last week spending the United States on the future of their high-quality education in New York. The fact that the difference in education between the different universities in Iran for the next year, in one of the universities in the United States that have been chosen, the special relations that have been established so that more information and experiences can be more beneficial to the future of our services and more effective. Today, 22 people from Iran are living in poverty from Shoradi, who are free to live in their own poverty. These 22 people are the representatives of thousands of Iranians who, most of them in their youth, have become the best of them during their time in Shoradi, living in poverty, poverty, poverty, and poverty. The United States of Shahan Shahi of Iran for Iranians living in poverty from Shoradi, living in poverty, poverty, poverty, in their own poverty, in their own poverty, is a great opportunity. I hope that the Iranian people will continue to live in poverty from the grace of safety, freedom, and security. The United States of Shahan Shah is the North wing trat In the United States of Shahan Shahi of Iranが私犠推の耕识 At last, under the supervision of Mr. Burji, the head of the entire Islamic State of Tehran, at the age of understanding and understanding, at the University of Pahitahumme, the majority of the students have been selected. Today, the increase of the number of students in the Islamic State of Tehran and the Islamic State of Tehran is the result of the new knowledge that has become a problem for the United States of America. In the next year, in the next year, in the new administration of Tehran, the head of the entire Islamic State of Tehran, only the members of the Islamic State of Tehran have been selected. There is no doubt that the number of students in the Islamic State of Tehran is the result of the full attention of the entire Islamic State of Tehran. The year of the election of 1338 and 1339 is the beginning of the election. In Paitahumme and the cities of Estonia, The U.S. is in Tehran for your warm-heartedness. This is a revolution. My dear son! Mashallah Baba! Don't you worry! May God protect you from the war! May God protect you from the future! These children have been raised in the presence of their parents and great children. And in the absence of their parents, they have become leaders. The U.S. is in Tehran for your warm-heartedness. Hill and Gully Rider, Hill and Gully. The U.S. anti-Iranian anti-Iranian variant, which was published in Tehran a few days ago, has been proven to be a good example for the people of Tehran to come to the scene again. The news of Iran has shown other parts of this variant for its dear viewers. The U.S. anti-Iranian anti-Iranian anti-Iranian anti-Iranian variant, and God forbid, it is confirmed to be a legal anti-Iranian anti-Iranian anti-Iranian variant. The families of these families had died in the name of the school in which many French-made anti-Iranian students were presented. It is also an American-made anti-Iranian anti-Iranian thatans the role of one of the U.S. US officials in Iran will be held on the 10th anniversary of the revolution. With the anniversary of the murder of Mr. Hossein Hamadanyan Navazande Marouf, the program of the UNARI version of Iran-Iran will be broadcast to the public. I'm writing you a letter from a land not far away. A land that is rich and full of promise. The earth is fertile. In some places, the top soil is 30 feet thick. Three crops of corn can be grown in a year. Three crops of cotton, tobacco, sugarcane harvesting never stops. Above the earth and below it, riches to equal a king's ransom. The coffee, the world drinks, and the emeralds madame wears to the opera an opening night come from here. Here, from this land of potential abundance. I'm writing you this letter from Colombia. I have come here to make one of those films about progress that you see from time to time. New housing, industry, machinery. Progress with a big P that you can measure in tons of bricks and miles of road. This is about my search for that progress, what I found, and where I look to find it. Here there was much left to be done in this land where death was accepted as a part of daily life. These are children's coffins. The official face of progress is the inauguration where dignitaries speak at openings of new schools, or housing projects, or health centers. But what one needed to know when President Balanchier placed a brick in celebration of the 5,000th house to be built in one development was what is the real nature of Columbia's progress. A family of 12 crammed into a bamboo hut. They live here while they build a new home. The Colombian government has had an effect for some time, a program to provide housing for people like these. A loan is made to the family to build a home in a supervised housing development. In most cases, the people do the work themselves. This woman had eight children.  And for the first time in Columbia, I stopped to look closely at her face. Today, Columbia is a part of the Alliance for Progress, but long before any such alliance existed, Colombians had decided that they would progress. They worked out a plan to see what they could do themselves to take the steps so vitally needed to make Columbia into a modern nation. The Calca Valley. Hundreds of square miles of the richest farmland on earth, badly farmed, badly irrigated, much of it lay in waste. The Colombian plan started with the land. Along the Calca River, pumping stations are being constructed as part of the enormous Calca Valley flood control land reclamation project, which is now underway. The development of the valley is making new industry possible. The establishment of new plants, which will not only provide jobs on their own right, but will stimulate jobs in other fields better utilizing the strength of the nation and giving the worker better pay. While that goes on, others are learning more about the earth beneath their feet. How crops grow, how to grow new ones. There are three schools in Columbia now forming young men into teachers of agriculture. Many of them begin training as young boys. They will stay five years. They come from families that earn only a few cents a day from a few rows of potatoes on a hillside or from a little bit of platinus or sugar cane or a few coffee trees badly cared for. A few orange trees growing wild.  Remember that look. We'll find it later somewhere else. After five years, the students become teachers in small villages, rural areas. They use their knowledge to awaken interest in the community and new farm techniques instructing children in modern farm practices and the adults in the solutions to their particular problems.


Can XRP realistically hit $100 during the next bull run? In today's video, we're going to take a realistic view on whether or not XRP can hit $100 and what it would take for something like that to happen. What's up guys? My name is Jay and welcome to Bitcoin Daily. If you guys are new here, don't forget to subscribe and smash that like button. Also turn on the notification so you can stay up to date with everything crypto. So first, let's understand exactly what XRP Ripple is all about. XRP was created by Ripple Labs Incorporated, a technology company based in San Francisco. It was formed back in 2012 by Chris Larson and Jed McCaleb. Now it's important to clarify a common misconception. Ripple and XRP while related are not exactly the same. Ripple is the company that created and uses the XRP token in its product. So when we talk about XRP, we're referring to the token or the cryptocurrency not Ripple Labs. Now with that out the way, XRP was designed to enable faster direct asset transfers that are settled within seconds. It's also scalable, capable of handling 1500 transactions per second 24-7. Now let's talk about the Ripple network known as RippleNet. RippleNet is Ripple's network of institutional payment providers such as banks and money service businesses that use solutions developed by Ripple to provide a seamless experience to send money globally. It's designed for enterprise use and provides real-time on-demand payments between participants in the network. So now that we understand what XRP Ripple is, let's move on to the current state of XRP Ripple. Ripple is trading at 64 cents with a market cap of $33.8 billion making it the fifth largest cryptocurrency in the market today. Now if we look back at XRP's performance over the past few months or even years, it's been quite a rollercoaster ride to say the least. We've seen it hit some highs but also seen it hit some notable lows. Remember it's essential to note that the price of XRP just like every other cryptocurrency is very volatile and is influenced by a wide variety of factors such as market sentiment, economic conditions, regulatory news and more. A significant factor that has impacted XRP's price over the last few years is its case against the SEC. The SEC filed a lawsuit against Ripple Labs and two of its executives in December of 2020 alleging that they conducted a $1.3 billion unregistered securities offering. The lawsuit created a lot of uncertainty around XRP and a bunch of exchanges in the US even delisted XRP. However, recently a judge wrote that direct sales of XRP to institutional investors were sales of unregistered securities. However, all other sales and in particular sales of XRP through exchanges to retail investors were not sales of unregistered securities. This was a massive win for XRP which shot the price up over 90%. This ruling led the biggest exchanges in the US to relist XRP. So now the big question that I've been getting is can XRP actually hit $100 in the next bull run? So to understand that we need to understand the math behind it. Currently XRP has a circulating supply of about $52.7 billion. So for XRP to reach $100 the required market cap would need to be around $5.3 trillion to put that into perspective. As of the time of recording this video the entire cryptocurrency market cap is roughly $1.18 trillion. So for XRP to hit $100 not only would it need to be the entire market cap of cryptocurrency right now but it would need to be five times more that. Now if we're expecting Bitcoin to hit $100,000 during the next bull run and I feel like this is a conservative number. So right now Bitcoin's market cap is at $582 billion while XRP is at $33.7 billion. $33.7 billion is about 5.8% of Bitcoin's current market cap. So if we're thinking that Bitcoin's gonna hit $100,000 in the next bull run that would put Bitcoin's market cap at $1.9 trillion. Now 5.8% of $1.9 trillion would put XRP at about $110.2 billion which would put XRP's price at about $2. Now I know you guys are thinking during the last bull run XRP almost hit $2. Check this out. We're looking at a historical snapshot of XRP when it was at $1.56. At the time the market cap was about $70.9 billion. Even if we put the market cap right now to $70.9 billion, the price for XRP would be $134 billion. That's like at 2017-2018 when XRP hit a high of over $3. XRP's price here was $3.37, $130.8 billion. If XRP went to $130.8 billion market cap, today it would be about a dollar less than it was back in 2018 when it set that all-time high at $2.48 and the reason why is because of the circulating supply. The circulating supply back then was at $38.7 billion. The circulating supply now is at $52.7 billion and that number is only going to continue going up in the next two years when we're expecting to have that bull run peak. And of course during bull runs when out-season happens, Bitcoin also loses dominance against outcoins like XRP. But even if we doubled that 5.8% to let's say 10% at $220 billion market cap, that still puts XRP at only $4, definitely a new all-time high but nowhere near the $100 mark. And if you want to even say that XRP could potentially have 20% of Bitcoin's market cap at its all-time high, even at $380 billion market cap, which is 10x from where the market cap currently is right now, XRP's price still only gets to about $7 and that's not accounting for circulating supply growing. So all the way when against the SEC could definitely boost confidence in XRP and could lead to renewed interest and fuel more demand for XRP by institutions, taking into account new partnership, possible technological advancements within the Ripple network. I still think that reaching $100 is a very, very big long shot. Not something I'm expecting to see over the next bull run in the next two years but maybe something that happens over the next 10, 15, 20 years when the overall crypto market grows into a 10 or 20 trillion dollar market. So we've definitely covered a lot in this video. From what XRP is, its current state, its potential for reaching $100 and the possible realistic roadblocks that it might face. Now, as of the big question, can XRP hit $100? While the potential is there given the right set of circumstances, the current market conditions and the math just doesn't check out right now. Remember that this is just my personal opinion and not financial advice. I would love to hear your thoughts and comments on XRP. Do you think that it could hit $100? What factors do you think that could drive it to reach such prices? Or do you see the same roadblocks that we have covered here? Let's continue this conversation in the comments below. I read all your comments and replied to as many of them as I can. If you have found this video informative, please smash that like button and share it with your friends. If you haven't subscribed yet, consider doing so. And if you're looking to find the next 100X crypto, I have found a way to leverage millions of dollars in research to find that next 100X project. In this recent video, I show how to leverage the research and investments of three of the world's leading venture capitalist firms in crypto. Click on the video on the screen right now and I'll see you guys there. As always, peace and love.


So, the next topic we want to talk about is inequalities, statistical inequalities. And of course, one we have already seen which is the Cauchy-Schwarz inequality, but there are some other important ones which we will talk about now. Now, the role of inequalities is that you get bounds on probabilities of certain events and this is different from the approximations. Because the inequalities make a very definite statement, so it is a definite fact about randomness. So, you have some event and you want to, you are able to say that the probability of this event will be less than or equal to a definite number. So, you give a bound and or lower bound, upper bound whatever is possible, mostly we will see that we talk about upper bounds. So and of course, another thing is that this is different, the inequalities give you information which is different from approximations, because approximations may be good, bad, but here the inequalities trying to tell you the probability of a certain event is less than this particular number, which the approximation does not say, approximations says that the probability may be this and then depending on. So, therefore they have a very definite role to play the inequalities in your statistical analysis of data and so on. So, see what happens is that when in the absence of much knowledge about the distribution of sample values, you take different kinds of samples and then you do not know much about the distribution of the population from which you are taking the samples. And then to derive bounds for probabilities of events, you know depending on the sample values is very helpful and that is what we do through these inequalities. So, in fact, it may just happen that we may know the mean or the variance of the population of which the sample values are coming and that is it, we may not know the nature of the distribution exactly. So, then it helps to be able to compute the compute bounds of the probabilities of certain events. .. So, the first one simple one is Markov inequality and this statement is that if x is a random variable that takes only non-negative values, then for any real number a greater than 0 probability x greater than or equal to a is less than or equal to expected x upon a. And this is not difficult to prove because if you know you define this indicator valuable where variable, so which is which takes value 1 when x is greater than or equal to a and 0 otherwise. So, that means, so now when you write x greater than or equal to a this implies that 1 is less than or equal to x by a that is and since i is equal to 1 whenever x is, so that means I can write that i is less than or equal to x by a. Now, taking expectation of both sides, so when I take expectation of both sides I get expectation i which is less than or equal to expectation x by a, but expectation x by a is 1 by a expectation x right. So, this I am just relating the two random variables i and x, so this is 1 by a this and expectation i would be because this is i is equal to 1 with probability x greater than or equal to a, so the expectation would be 1 into probability x greater than or equal to a plus x equal to i equal to 0 probability that x is less than a. So, but since i is 0, so that is no contribution, so expectation i is actually equal to probability x greater than or equal to a into 1 right. And where did we use the fact that it is a non-negative variable, I used it from here saying that if i is less than or equal to x by a then the expectation will also when I take the expectation of both sides the inequality will remain intact. And therefore, this is less than or equal to 1 by a e x or probability x greater than or equal to a is less than or equal to 1 upon a into expected x. So, you see for this event just knowing that just knowing the expectation of the random variable I can compute a bound for the probability of this event which is given by 1 by a into e x. So, let us look at this Chebyshev's inequality which says that if x is a random variable with finite mean mu and variance sigma square then for any k positive expectation of x minus mu absolute value greater than or equal to k sorry it should not be expect probability. We are Chebyshev's inequality is for giving an upper bound on a certain probability which is probability absolute value of x minus mu greater than or equal to k is less than or equal to sigma square upon k square. So, mean x has mu as its mean. So, when you take so actually this can also be written as expectation of x minus mu whole square and then divided by k square. So, that is the variance and of course, I do not need the absolute sign once I am taking square. So, this is actually expectation of whatever the function here. So, you are taking x minus mu. So, expectation of this whole square divided by k square. So, we are defining this for mu as the mean of x and k is some positive number. So, this is the inequality. So, that means this gives you a bound the inequality gives a bound on this probability which has to be less than or equal to sigma square by k square. Now, we will use Markov's inequality to prove this we just established Markov's inequality. So, now, let me define y as x minus mu whole square and this will be therefore, non negative and the Markov's inequality requires is defined for is valid for random variable which takes only non negative values which is greater than or equal to 0. Then we will take a to be k square and so, then the Markov's inequality will give us that probability x minus mu whole square greater than or equal to k square is less than or equal to expectation of x minus mu whole square by k square. Expectation of this divided by k square e x. So, this is e x by a where this is a and this is your x. So, then I am writing my x is x minus mu whole square. So, expectation of x minus mu whole square by k square. So, by Markov's inequality this and then you are saying because my a is k square and my x is x minus mu whole square. Now, just see that this event x minus mu whole square greater than or equal to k square holds if and only if this holds for since k is given to be positive. So, if this is true then this is true if this is true then this must be true. So, if they are the same events and therefore, I can replace this probability by the probability absolute value of x minus mu greater than or equal to k this is less than or equal to sigma square by k square. So, the inequality is established and then we will through examples and so you will see the various ways in which this simple inequality can be used. Now, the thing is I just want to make a note here that often we are asked to obtain a bound for a probability like this which has a strict inequality. So, this is probability of x minus mu absolute value of x minus mu greater than k. But, then we know that this probability is less than or equal to probability of absolute value of x minus mu greater than or equal to k because you are taking a bigger subset here. So, this probability is this probability is bigger than this probability and hence and since we have a bound for this through ship in equality. So, the bound is also valid for this probability. So, that means we can say that probability mod x minus mu greater than k is also less than or equal to sigma square by k square this is the whole idea. And through when we discuss many examples it will turn out that we have to actually compute this a bound for this probability. And so we will see that this can be again estimated by I should not use the word estimate because this probability is less than or equal to this and Chebyshev's inequality gives as a bound for this. So, therefore, the same bound is valid for this probability also. Now, one can also obtain I mean one can there are more than one ways of obtaining these inequalities. And so I will just give you the alternate proof which says that if so I will start with the expression for sigma square which is expectation of x minus mu whole square. So, you are taking k on either side. So, now I can break and this integral will be minus infinity to infinity of x minus mu whole square f x d x. So, this integral I break up into so minus infinity to mu minus k that means this point and then it will be mu minus k to mu plus k and then mu plus k to infinity. So, I break up the integral. So, the total integral minus infinity to infinity I break it up to these three. Now, if you look at this expression for example, here x is greater than mu plus k it is going up to infinity and remember k is a positive number.  So, it actually this is implied. So, if this wherever x is greater than mu plus k it means that x minus mu is greater than k and similarly here your x is less than mu minus k. So, for x less than mu minus k it implies that your x minus mu is less than minus k.  So, this must be a non negative quantity it cannot be negative because this is non negative this is non negative. And so therefore, the equality if I remove this then the inequality changes to inequality. And secondly as we said that in this interval mu plus k to infinity x minus mu is greater than k. And so here again f x is a non negative function. So, if I replace this by k square then I am taking a lower value of the whole integral.  So, square would be what will happen to square x minus mu whole square will become greater than k square.  So, when I square up x minus mu whole square will be greater than k square. So, then if for in both these integrals I replace x minus mu whole square by k square I am taking the lower value under estimate of the integral.  But this is nothing but k square of course is a constant. So, this is probability x less than or equal to mu minus k plus this is probability x greater than or equal to mu plus k mu plus k to infinity. But then if you bring mu to this side this will be probability x minus mu less than or equal to minus k here this will be probability x minus mu greater than or equal to k. So, probability of absolute value of x minus mu greater than or equal to k. So, what is written is the strict inequality, but it should actually be probability of mod x minus mu greater than or equal to k. So, we have the inequality sigma square greater than or equal to k square probability of absolute value of x minus mu greater than q k. And so, that gives us the inequality that we wanted to prove. So, this is the Shebyshev's inequality this again gives you an upper bound on the probability mod x minus mu greater than or equal to k once we know the variance of the random variable x. So, this proof can be imitated for the discrete case also that is when x is a discrete random variable with finite variance and there will be a probability mass function also defined with it. The immediate corollary is that if you put k equal to epsilon sigma where of course, epsilon is some non negative number then the Shebyshev's inequality becomes greater than or equal to epsilon sigma this is less than or equal to sigma square upon epsilon sigma square which is 1 by epsilon square. And if I divide here by sigma sigma being a non negative positive number. So, inequality does not change and probability x minus mu by sigma. So, this is you can say standardized variable your standardized variable x. So, this greater than or equal to epsilon is less than or equal to 1 upon epsilon square simple version of the simpler version of the Shebyshev's inequality. So, we would like to now work out some examples to see how these bounds can be used. So, let us consider a few examples on this inequalities that we have just discussed. This example says that x is a random variable with mean and variance both equal to 16. So, compute a lower bound on probability that x lies between 0 and 32 using Shebyshev's inequality because here we cannot use Markov's inequality right. It is a two sided thing and yes and again fine. So, therefore, we will use the Shebyshev's inequality here. The solution says that you convert this probability to probability of 0 minus 6. So, it just divides subtract 16 from both the sides. So, it will be probability 0 minus 16 less than x minus 16 which is less than 32 minus 16. So, the two events are the same and then this reduces to probability of absolute x minus 16 is less than 16 right. This is minus 16 and this is 16. So, absolute. So, now, this is in the form of well this is the opposite of the what we compute the lower bound for greater right. So, now, here I will have to write this as 1 minus probability absolute x minus 16 greater than or equal to 16 right. We had strict inequality here. So, this was strict and therefore, the opposite event would be the converse or the complement event would be absolute x minus 16 greater than or equal to 16 right. And since Shebyshev's inequality gives us a lower bound. So, therefore, when I write down sorry gives an upper bound. So, when I replace this by its upper bound minus of that will become. So, smaller way. So, the inequality the equality here will change to greater kind right. Because I am writing see this is for this I am writing a bigger number, but the minus will become a smaller number and therefore, this probability will be greater than or equal to 1 minus expectation of x minus 16 whole square divided by 16 square. But this we know is the variance of x which is 16. So, therefore, this is 1 minus 16 upon 16 square and. So, this is 15 by 16 and you can see that it is a fairly loose bound. So, 15 by 16 is a number close to 1 yes and there will be. But anyway. So, trying to show you that these bounds that you get are rather loose they are not very tight, but at some situations they are quite helpful also. Now, another example is from past experience a professor knows that the test score of a student taking her final exam is a random wearable with mean 65 that is not bad. If the mean is 65 then out of 100 then the students are good. So, let us see give an upper bound for the probability that a student's test score will exceed 85. So, you need an upper bound for the probability. So, therefore, we just know that the mean is 65 and that is it and using that we compute. So, here you will to answer this you will simply use Markov's inequality and that will give you probability x greater than 85. So, your a is 85 and so this will be less than or equal to expectation x upon 85 which will be 65 upon 85. So, 13 by 7. Now, Markov's inequality says that probability x greater than or equal to a is less than or equal to expected x by a. But we can also use this Markov's inequality for computing an upper bound for the event x for the probability of the event x greater than a. Since probability x greater than a is less than or equal to probability x greater than or equal to a. So, therefore, probability x greater than a will be less than or equal to expected value of x divided by a. So, therefore, when to compute the upper bound for the probability x greater than 85 I could use the number e x divided by 85 and this is what we will use for the for future computations also that follow. So, this is the answer that you get from Markov's inequality. Now, if there is an additional information that the professor knows that the variance of a students test score is equal to 20. So, if you have knowledge of the variance then you can use Shevyshev's inequality and then you will say that probability absolute x minus 65 is greater than 20. So, this probability will be less than or equal to expectation of x minus 65 whole square upon 20 square because this is your k. So, that is 20 square and therefore, since we know that the variance of x is x obviously, is the test score. So, then that is 20. So, 20 upon 20 square this is 1 by 20 of course, the numbers are little contrived does not matter. So, and then see the this event is actually probability x minus 65 greater than 20 either this is greater than 20 or this is less than minus 20. So, and you were looking for this probability, but in any case this is probability x minus x is less than 45. So, I could write plus here because the two events are disjoint. So, in other words if you want a bound for probability x minus 65 x x. So, this will give you a probability x greater than 85 plus probability x less than 45 which is 1 by 20. So, in other words your probability x greater than 85 is less than or equal to 1 by 20 because this will be something positive. So, you subtract from 1 by 20. So, therefore, this bound is definitely I mean there is a dramatic difference between 13 by 7 and the number which is 1 by 20. So, you see the moment you have more information about the distribution about the random variable you can get better bounds for the bounds are tighter. So, this was just I think I just sat down and contrived these numbers and so they may not be look very realistic because 20 is probably a high number for the variance. And therefore, so therefore, there is a dramatic change because you see this had no knowledge of the variance. So, I just computed this. So, this number we computed knowing the expected value. So, if here the variance is much smaller then obviously, this probability will also be this bound will be higher fine. So, this is just to show you that the difference between the two bounds. Now, the second part of the problem is that how many students will have to take the exam to ensure with probability at least 0.9 that the class average would be within 5 of 65. So, how many students? So, suppose we assume that there are n students who are taking the exam and then the class average would be given by. So, class average would be summation x i i varying from 1 to n divided by n which in our notation we can also write as x bar. So, that will be your class average and so what they are saying is that the class average which should be within 5 of 65. So, it is either 5 less than 65 or 5 more than 65. So, therefore, this class average should be within 60 and 70. So, this is a probability that you have to. So, you are told that this probability should be at least 0.9 and then you want to know how many students should take the exam. So, that this probability is at least 0.9 that means it is greater than or equal to 0.9. So, here again I am trying to standardize or get it in the form of the Shebyshev's inequality. So, we will. So, x bar minus 65 because mu of x bar is expected value of x bar is also 65 since each x i is. So, therefore, this will be 60 minus 65 less than or equal to x bar minus 65 less than or equal to 70 minus 65. And then I can also here divide by. So, what is the variance of here variance x bar will be variance of each x any of the x i is the same divided by n. So, because n variance x i is divided by n square. So, this becomes this and so under root of this. So, that will be under root of 20 by n. So, if I divide both sides by under root of 20 by n the inequality even does not change. So, this is what I have now and this is 1 minus probability x bar minus 65 upon under root 20 by n. So, this gives me that means now this is my I mean applying Shevyshev's inequality here this is greater than 5 by under root 20 by n. So, this would be by again because I am writing 1 minus of this. So, if you have less here that means this is less than some number by Shevyshev's inequality. So, minus that will become greater and so this is 20 by n into 25 because what is the have I written it correctly here. So, you want to by Shevyshev's inequality this would be what this is this number if I just write this number this is less than or equal to expectation of x bar minus 65 upon 20 by n this whole square divided by you can say 25 n by 20. But, this has variance 1. So, actually it should be yes. So, see this is this has variance 1 because I have standardized it. So, expectation x bar minus 65 upon under root 20 by n whole square has variance 1. So, the number is 20 upon n 25 and so this should be and this is greater than or equal to. So, my probability and therefore, if I put this equal to 0.9 then my this at least part is satisfied right. And so the value of n that gives me this quantity equal to 0.9 will satisfy because the probability that I have written on the left hand side is greater than or equal to this. 20 upon 25 n equal to 0.1 implies n is equal to 8 and not 80 as written. Therefore, for n greater than or equal to 8 the class average will be within 5 of 65. So, you know lots of different kinds of probabilities you can obtain via you know using the Shevyshev's inequality you can get the bounds you can get estimates of the numbers and so on. So, let us consider this example it says that it cost rupees 1 to play a slot machine. See now some of you have an idea that you put in 1 rupee and then if you are lucky some money comes out otherwise nothing comes out. So, the machine is set by the house. So, wherever you are this slot machine is put the machine is set to pay rupees 2 with probability 0.45 and nothing with probability 0.55. So, you see you put in a rupee and then with probability 0.45 you expect to get 2 rupees otherwise with the probability 0.55 you do not expect to get anything. So, you lose that rupee fine. So, find approximate probability that after 10,000 plays of the machine the houses winnings are between rupees 800 and rupees 1200. So, you see winnings means that when the house has to pay to the player then it is losing. So, since when the player puts in 1 rupee and the house has to pay 2 rupees then that is a loss for the house. So, therefore, x i is equal to minus 1 is with probability 0.45 and x i is equal to 1 with probability 0.5. So, this represents the earning of the machine you know in the i th play of the game when the slot machine is being played for the i th time. So, x i is equal to minus 1 with probability 0.45 and this is 1 with probability 0.55 and of course, you can see that e x i the expected value of x i will be minus 1 into 4.45 plus 1 into 5 5. So, this is 0.1 as you expect because otherwise why would people or house want to invest money in a slot machine if the expected earning is not positive. So, this is 0.1 per game of the slot machine and similarly the variance x i would be 0.99 because it will be expectation x i square. So, once you put x i square then this will become plus 1 into 0.45 plus 1 into 0.55 which will be 1. So, expectation x i square is 1 and then expectation x i whole square will be 0.1 square. So, this becomes 0.99. So, the variance of each x i is 0.99 and earnings of the house are represented total earnings are 1 to 10,000. So, sigma x i summation from 1 to 10,000 gives you the earnings of the house in which losses and income are included. The net net income the net earning of the house is sigma x i i varying from 1 to 10,000 and so expected value of the earnings is rupees 1,000. Because this is 0.1 0.1 multiplied by 10,000 which gives you rupees 1,000 and the variance sigma x i is 9900. Now, I have not standardized this here it is to carry on the computations with these values. So, now we have to compute the probability that total earnings of the house lie between rupees 800 and 1200. So, here again we will do the same thing we will try to standardize this probability and so I will subtract the expected value of sigma x i which is 1,000 rupees on either side. So, that gives me that absolute of sigma x i I varying from 1 to 10,000 minus 1000 is less than 200. So, again we have it in the right form in the sense that now I will write this as 1 minus probability sigma x i I varying from 1 to 10,000 minus 1000 should be greater than or equal to 2. So, it is saying between 800 and 1200. So, I am taking strict inequality here. So, therefore, the complement event will have greater than or equal to 200. So, I have set it right for the use of Shebyshev's inequality. So, again the same reasoning that this thing is less than I get a lower upper bound. So, therefore, minus of that will give me the lower bound. So, minus of that. So, therefore, this will be this is less than or equal to variance of x i sigma x i divided by 200 square. So, variance of sigma x i is 9 to see remember this is 99,000 9900. So, therefore, this is greater than or equal to 1 minus 9900 upon 200 square which is equal to which is equal to 1 minus 9900 upon 40000. And so, this becomes this. So, again that means this close to 0.75 the probability. So, you would expect that because 10000 plays and you know the machine the expected value from each play of the machine is 0.1 expected earning. So, therefore, this is probably not a very bad bound. So, at least. So, here of course, the probability is at least 301 upon 400. It can be more. So, it is understood that the Shebyshev's bounds are not very tight, but it gives you an idea. It gives you a feeling about the probability of the event that you are trying to estimate. Another example because I feel that there are so many different situations where you have to learn to how to compute the how to make it how you can apply Shebyshev's inequality. And therefore, I just collected a lot of different examples. So, let us look at another example here which says that a fair die is rolled. And what we mean by independently 3 times which means that there is no bias and so the outcomes are independent. So, the outcomes of when the dies rolled 3 times whatever the outcomes are independent outcomes. Now, we define x i as 1 the i th roll yields a perfect square. So, x i denotes the random variable which is equal to 1 if the i th roll gives me a perfect square and 0 otherwise. So, first find the PMF of x i and I need to do all this work before I apply the Shebyshev's inequality. So, the PMF of x i and then y is equal to x 1 plus x 2 plus x 3 then you have to find the PMF of y and then verify Shebyshev's inequality. So, we will compute the actual probability and then also get the bound by the Shebyshev's inequality and compare. So, obviously, we expect that since this gives us a upper bound. So, the actual probability that we compute will be less than what we get by the Shebyshev's inequality. This is the whole idea and I thought that we can if you work out in detail you will get a good feeling about the whole thing. So, anyway so let us see the solution procedure.  So, 1 and 4 are the only perfect squares and therefore, probability x i equal to 1 will be 2 by 6 which is 1 by 3 and probability x i equal to 0 will be 4 by 6 which is equal to 2 by 3 for all i and i's are also and x i's are independent. So, now you take y to be x 1 plus x 2 plus 3 and y i takes values 0, 1, 2 and 3 because none of the die show a perfect square. So, then this value is 0, one of them shows a perfect square, two of them show a perfect square or all three show a perfect square. So, the possible values of y are 0, 1, 2 and 3 and they are not difficult to compute the PMF of y because y equal to 0 means that all three variables take 0 value and since they are independent therefore, it will be product of probability x 1 equal to 0, x 2 equal to 0 and so that x 3 equal to 0. So, it will be 2 by 3 square which is a cube. So, which is 8 by 27, similarly probability y equal to 1 will be see now here I just take this case that x 1 is 1 and x 2 and x 3 are 0, then there can be three such combinations where one of them is 1 and the other two are 0. So, this will be 3 times this particular probability which is again using independence x 1 equal to 1 is 1 by 3. So, 3 times 1 by 3 into this is 2 by 3 raise to 2 which is 4 by 9. So, the probability is 12 by 27 and y equal to 2 again the same case that if I take this particular event x equal to 1 equal to x 2 and x 3 is 0, then again the three combinations which will give me the same value for y which is equal to 2. So, 3 times probability x 1 equal to 1 equal to x 2 and x 3 equal to 0. So, this will give me 3 into 1 by 9 into 2 by 3 x 3 equal to which is 6 by 27 and probability y equal to 3 requires that all three must be equal to 1 and that probability will be 1 by 27. Now, you can just make sure that you have got computed the right PMF by adding up all these probabilities. . So, 7 plus 6 13 plus 12 divided on this is 1 and 6 sorry 1 and 6 7 7 and 12 7 and 12 19 19 and 8 27. So, all these probabilities add up to 1. So, this is the right PMF. Now, therefore, we can immediately compute expected value of y which is 1 I mean I leave that to you because now you have the probabilities multiply by the corresponding value of y and you add up and get this and similarly, expected value of y square is 45 by 27. So, the variance comes out to be 18 by 27. So, now for example, probability y minus 1 greater than half if you want an estimate for this upper bound then this is less than or equal to expected value of y 1 whole square y minus 1 whole square into 4 1 by 2 square which will become in the denominator will become 4. Now, this certainly there is no verification is needed because the actual probability cannot be more than 1 whereas, this number is coming out to be more than 1 because you are you have put a number 1 by 2 here are you ok with this because 4 into 87 by 27 this number is greater than 1. So, here I do not need any verification. So, more meaningful verifications will be when for example, I want to say that probability y minus 1 absolute value greater than 1 is less than or equal to. So, this will be variance y upon 1 which is 18 by 27. So, now we will actually compute this probability and show that it is less than 18 by 27 to make sure that this is this actually gives you an upper bound. If you observe that b is y is also distributed has a binomial distribution a binomial distribution with the parameters 3 1 comma 3. So, the probability of success is given by 1 by 3 and number of rolls is number of rolls is 3. Now, and therefore, immediately you know that hence expected value of y will be n p. So, 3 into 1 by 3 is 1 and the variance of y will be 3 into 1 by 3 into 2 by 3 n p q which is 2 by 3 and, but we computed this independently as 18 by 27 which is also 2 by 3. So, fine anyway now just want to we are we are testing the we are comparing the actual computations of probabilities with the Shevyshev's bounds. So, if you want to look at this probability absolute value of y minus 1 greater than or equal to 1. So, you see that here y minus 1 greater than or equal to 1 implies that y can take the value 0, 2 and 3 because y is 0 then absolute value of minus 1 is 1. So, which is equal to 1. So, remember the event is greater than or equal to therefore, y can be equal to 0, 2 and 3 and in that case this probability will be equal to probability y equal to 0 plus probability y equal to 2 plus probability y equal to 3 and. So, we make this computation 8 by 27 plus 6 by 27 plus 1 by 27 which is equal to 5 by 9, but if you compute the Shevyshev's bound then this will be variance y upon 1, 1 square is 1 and this is variance y which is 18 by 27 or 2 by 3.  See, 15 is less than 18 when you compare 5 by 9 is less than 2 by 3 and then let us see take another event. So, this is this will be probably absolute value of y minus 1 greater than or equal to 2 which is simply probability y equal to 3. So, we can use the binomial probabilities here and so y equal to 3 would be simply 1 upon 27, 1 by 3 raise to 3 and this by the Shevyshev's inequality will be variance y upon 4 because your k is 2. So, this is 18 by 27 into 1 by 4 which comes out to be 1 by 6 and so when you compare 1 by 27 with 1 by 6 the gap widens. This is a loose upper bound by the Shevyshev's inequality and now if you want to look at the event probability absolute value of y minus 1 greater than or equal to 0 then we cannot apply the Shevyshev's bound because this number has to be positive. Remember k greater than 0 so that is required. So, therefore, I cannot compute a bound for this. So, you may compute the actual probability here, but Shevyshev's bound cannot be computed. What I have tried to show you is of course, through various examples how to get the probability required to compute the lower bound by Shevyshev's inequality. So, doing that and then also try to give you a feeling that the bounds we are computing are loose bounds, they are not tight ones. And thirdly now what we will I would like to show you in the next lecture is that apart from computing bounds it has also proved a very useful tool for showing you know we will be talking of convergence theorems in the next lecture. And that is where I will show you how useful a tool the Shevyshev's inequality is and so that will be the next.


So this question says, a hospital x-ray gun that has a wavelength of 15.0 nanometers emits x-rays. What is the energy of one of these x-ray photomic particles? So anyways, what we have to remember is two equations. So E equals N, H, nu, C equals lambda, and nu being the frequency and lambda being the wavelength. So if we rearrange this equation, we get nu equals C over lambda. So we're going to plug that into this equation. So N, H, C divided by lambda. OK, H and C are constants given to you. So C, 2.998 times 10 to the 8 meters per second. And H is Planes constant, so this is to be like 6.626 times 10 to the negative 34 joules seconds. So N in this case, since it just wanted one photon, was 1. That should give us everything we need, because we've got wavelength here. The only thing that is the problem is that we've got this C in meters and wavelength in nanometers, so we're going to have to convert nanometers to meters. So how do we do that? If you don't remember, this is one that you want to remember. So there's 1 times 10 to the 9 nanometers per 1 meter. So let's go ahead and plug all of that into the calculator and see what we get. OK, so well, we don't have to convert it. Joules is the energy unit in 1. So H is 6.6234, and that's C, 2.998 times 10 to the 8 to the power 1 second. And then 1 over lambda 1, it's upset. OK, so if we look here, we've canceled seconds there, meters there, and we get joules for our units. That's good energy units. It didn't say to give it in kilojoules or millijoules or anything like that, so let's just stick with joules. So this is just one photon, so we would expect it to be a very small number. And the number I got to 3 sigma bigs is 1.32 times 10 to the negative 17 joules per x-ray photon. OK? I just wanted to know, how do you know it's a 1 photon? But can you just assume that, because it's an accident? Yeah, so when it doesn't ask you, it's expecting you to do one photon. It'll tell you sometimes it'll say, what's the energy of one mole of photons? And in that case, you do 6.022 times 10 to the 23rd. You just got to remember this. That's where I didn't know where to plug in, because I didn't know what to do with n. That n there, you just got to watch it, OK? So that's the number of, in this case, photons. That's what I meant. That's a specified one. Yeah, just choose one, yeah? Any questions on that one? OK.