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Eğitmen, önceki videolarda tek random variable kullanırken, bu videoda iki farklı random variable kullanarak marjinal ve şartlı olasılık kavramlarını açıklamaktadır.","Video, marjinal olasılık kavramını tablo üzerinden detaylı şekilde ele almakta ve ardından şartlı olasılık kavramını \"Friends\", \"Rick and Morty\" ve \"Black Mirror\" dizileri üzerinden örneklerle açıklamaktadır. Eğitmen, marjinal olasılığın nasıl hesaplanacağını, satır ve sütun toplamlarının nasıl bulunacağını ve şartlı olasılık formülünün (P(A|B) = P(A ve B) / P(B)) uygulamalı olarak nasıl kullanılacağını adım adım göstermektedir.","Videoda ayrıca marjinal olasılığın sürekli durumlar için integral kullanılarak nasıl hesaplanacağı, marjinal olasılık dağılımının toplamının 1 olduğunu ve bu dağılımın marjinal olasılıkların toplamı olduğu vurgulanmaktadır."]},"endTime":938,"title":"Marjinal ve Şartlı Olasılık Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Marjinal ve Şartlı Olasılık Kavramları","list":{"type":"unordered","items":["Marjinal ve şartlı olasılık kavramları, iki farklı rastgele değişkeni içeren bir tablo üzerinden açıklanacaktır.","Tabloda iki farklı rastgele değişken bulunmakta ve her bir değer için olasılık değerleri verilmiştir.","Tabloda bulunan altı değer, ortak olasılık dağılımını oluşturur ve bu değerlerin toplamı bir eder."]},"beginTime":0,"endTime":139,"href":"/video/preview/10498071285644325713?parent-reqid=1769649298363999-514366473176398324-balancer-l7leveler-kubr-yp-sas-15-BAL&text=Marginal+Boundaries&t=0&ask_summarization=1"},{"index":1,"title":"Marjinal Olasılık Kavramı","list":{"type":"unordered","items":["Marjinal olasılık, ortak olasılık dağılımından bir rastgele değişkeni çıkararak elde edilir.","Marjinal olasılık dağılımı, tüm olasılıkları göz önünde bulundurarak oluşturulan bir dağılım grafiğidir.","Marjinal olasılık dağılımının değerleri toplamı bir eder ve bu değerler, sadece belirli bir rastgele değişkeni incelemek istediğimizde kullanılır."]},"beginTime":139,"endTime":346,"href":"/video/preview/10498071285644325713?parent-reqid=1769649298363999-514366473176398324-balancer-l7leveler-kubr-yp-sas-15-BAL&text=Marginal+Boundaries&t=139&ask_summarization=1"},{"index":2,"title":"Marjinal Olasılık Hesaplama Yöntemleri","list":{"type":"unordered","items":["Marjinal olasılık hesaplaması için satırları veya sütunları toplamak mümkündür.","Aylık durumlarda toplama işlemi yapılabilirken, sürekli durumlarda integral kullanılır.","Sürekli durumlarda, x için y'ye göre veya y için x'e göre integral alınır."]},"beginTime":346,"endTime":587,"href":"/video/preview/10498071285644325713?parent-reqid=1769649298363999-514366473176398324-balancer-l7leveler-kubr-yp-sas-15-BAL&text=Marginal+Boundaries&t=346&ask_summarization=1"},{"index":3,"title":"Şartlı Olasılık Kavramı","list":{"type":"unordered","items":["Şartlı olasılık, bir olayın belirli bir koşul altında gerçekleşme olasılığını hesaplamak için kullanılır.","Şartlı olasılık formülü P(A|B) = P(A∩B) / P(B) şeklindedir, burada P(A|B) A olayının B koşulu altında gerçekleşme olasılığını gösterir.","Örnek olarak, \"Friends\" dizisinden kaç kişinin kadın olduğu sorulduğunda, örnek uzay sadece \"Friends\" dizisi olur ve olasılık hesaplaması bu dizinin kadın kişi sayısına göre yapılır."]},"beginTime":594,"endTime":636,"href":"/video/preview/10498071285644325713?parent-reqid=1769649298363999-514366473176398324-balancer-l7leveler-kubr-yp-sas-15-BAL&text=Marginal+Boundaries&t=594&ask_summarization=1"},{"index":4,"title":"Şartlı Olasılık Örnekleri","list":{"type":"unordered","items":["\"Rick and Morty\" dizisinde erkeklerin tüm izleyicilerin yüzde 55'ini oluşturduğu bilindiğinde, erkeklerin olasılığı 0,55 olarak hesaplanır.","\"Black Mirror\" izleyenlerden kaçının kadın olduğu sorulduğunda, olasılık hesaplaması \"Black Mirror\" izleyenlerin toplam izleyicilere oranı olarak yapılır.","Kadınlardan kaçının \"Friends\" dizisini sevdiği sorulduğunda, olasılık hesaplaması kadınların \"Friends\" dizisini sevenlerin toplam izleyicilere oranı olarak yapılır."]},"beginTime":636,"endTime":743,"href":"/video/preview/10498071285644325713?parent-reqid=1769649298363999-514366473176398324-balancer-l7leveler-kubr-yp-sas-15-BAL&text=Marginal+Boundaries&t=636&ask_summarization=1"},{"index":5,"title":"Şartlı Olasılık Formülünün Uygulanması","list":{"type":"unordered","items":["\"Friends\" dizisini sevenlerden kaçının kadın olduğu sorulduğunda, olasılık hesaplaması \"Friends\" dizisini sevenlerin toplam izleyicilere oranı olarak yapılır.","Formülde payda marjinal olasılık olarak yazılır, örneğin \"Friends\" dizisini sevenlerin toplam izleyicilere oranı 0,35 olarak hesaplanır.","Kadınlardan \"Friends\" dizisini sevme olasılığı sorulduğunda, olasılık hesaplaması kadınların \"Friends\" dizisini sevenlerin toplam izleyicilere oranı olarak yapılır."]},"beginTime":743,"endTime":803,"href":"/video/preview/10498071285644325713?parent-reqid=1769649298363999-514366473176398324-balancer-l7leveler-kubr-yp-sas-15-BAL&text=Marginal+Boundaries&t=743&ask_summarization=1"}],"linkTemplate":"/video/preview/10498071285644325713?parent-reqid=1769649298363999-514366473176398324-balancer-l7leveler-kubr-yp-sas-15-BAL&text=Marginal+Boundaries&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"11. 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Hazırlayan: Kemal Duran...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/222140/bada03e826a2946215c69c560bde6d03/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/iu5uGwEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"8","reqid":"1769649298363999-514366473176398324-balancer-l7leveler-kubr-yp-sas-15-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769649298363999-514366473176398324-balancer-l7leveler-kubr-yp-sas-15-BAL&text=videoid:3563688068466103757","teaser":[{"list":{"type":"unordered","items":["Bu video, bir eğitim içeriği olup, sürekli ortak olasılık dağılımından marjinal olasılık dağılım fonksiyonlarının nasıl bulunacağını anlatmaktadır.","Video, sürekli ortak olasılık dağılım fonksiyonunun tanımıyla başlayıp, marjinal olasılık dağılım fonksiyonlarının ne olduğunu açıklamaktadır. Ardından, marjinal dağılım fonksiyonlarının nasıl hesaplanacağı formüllerle gösterilmekte ve bir örnek üzerinden adım adım çözüm yapılmaktadır. Özellikle X'in marjinal dağılım fonksiyonu için Y'ye göre integral alınırken, Y'nin marjinal dağılım fonksiyonu için ise X'e göre integral alınması gerektiği vurgulanmaktadır."]},"endTime":685,"title":"Sürekli Ortak Olasılık Dağılımından Marjinal Olasılık Dağılım Fonksiyonları","beginTime":0}],"fullResult":[{"index":0,"title":"Sürekli Marjinal Olasılık Dağılımı","list":{"type":"unordered","items":["Sürekli marjinal olasılık dağılımı (marjinal probability distribution) konusu ele alınacaktır.","Sürekli ortak olasılık dağılımından marjinal olasılık dağılım fonksiyonlarının nasıl bulunacağı açıklanacaktır.","Sürekli ortak olasılık dağılım fonksiyonu, iki şartı sağlamalıdır: eksi sonsuzdan sonsuza integralinin 1 olması ve tüm değerlerin 0'dan büyük 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Örnek üzerinden X ve Y rastgele değişkenlerinin marjinal olasılık dağılımlarının nasıl hesaplanacağı detaylı olarak anlatılıyor. Video, bu konunun temel prensiplerini öğrenmek isteyenler için faydalı bir kaynak niteliğindedir."]},"endTime":556,"title":"Kesikli Marjinal Olasılık Dağılımı Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Kesikli Marjinal Olasılık Dağılımı Kavramı","list":{"type":"unordered","items":["Kesikli marjinal olasılık dağılımı (İngilizcesi: marjinal probability distribution) kavramı bu videoda anlatılacak.","Kesikli marjinal olasılık dağılımını anlamak için önce kesikli ortak olasılık dağılımı kavramını tanımlamak gerekir.","Kesikli ortak olasılık dağılımı, iki farklı rastgele değişkenin olasılıklarının aynı anda gerçekleşmesine ait olasılıkların oluşturduğu olasılık dağılımıdır."]},"beginTime":1,"endTime":48,"href":"/video/preview/5366639616594174763?parent-reqid=1769649298363999-514366473176398324-balancer-l7leveler-kubr-yp-sas-15-BAL&text=Marginal+Boundaries&t=1&ask_summarization=1"},{"index":1,"title":"Kesikli Ortak Olasılık Dağılımı Örneği","list":{"type":"unordered","items":["İki rastgele değişken X ve Y için bir kesikli ortak olasılık dağılımı tablosu oluşturulmuştur.","Tabloda X değişkeninin değerleri 1 ve 2, Y değişkeninin değerleri 1, 2 ve 3 olarak gösterilmiştir.","Tabloda yer alan olasılıkların toplamı 1 olmalıdır."]},"beginTime":48,"endTime":148,"href":"/video/preview/5366639616594174763?parent-reqid=1769649298363999-514366473176398324-balancer-l7leveler-kubr-yp-sas-15-BAL&text=Marginal+Boundaries&t=48&ask_summarization=1"},{"index":2,"title":"Marjinal Olasılık Dağılımı Tanımı","list":{"type":"unordered","items":["Marjinal olasılık dağılımı, kesikli ortak olasılık dağılımını oluşturan X ve Y rastgele değişkenlerinin sadece kendilerinin olasılıklarından oluşan dağılımdır.","Eğer kesikli ortak olasılık dağılımından geliyorsa, bu dağılıma kesikli marjinal olasılık dağılımı denir."]},"beginTime":148,"endTime":244,"href":"/video/preview/5366639616594174763?parent-reqid=1769649298363999-514366473176398324-balancer-l7leveler-kubr-yp-sas-15-BAL&text=Marginal+Boundaries&t=148&ask_summarization=1"},{"index":3,"title":"Marjinal Olasılık Dağılımı Hesaplama","list":{"type":"unordered","items":["X'in marjinal olasılık dağılımı, Y rastgele değişkeni ile beraber oluşan olasılıklar değil, sadece X'in kendi olasılıklarını gösterir.","X rastgele değişkeninin marjinal olasılıkları, tabloda X değerlerinin altındaki olasılıkların toplamı olarak hesaplanır.","Y rastgele değişkeninin marjinal olasılıkları, tabloda Y değerlerinin yanında olan olasılıkların toplamı olarak hesaplanır."]},"beginTime":244,"endTime":335,"href":"/video/preview/5366639616594174763?parent-reqid=1769649298363999-514366473176398324-balancer-l7leveler-kubr-yp-sas-15-BAL&text=Marginal+Boundaries&t=244&ask_summarization=1"},{"index":4,"title":"Marjinal Olasılık Dağılımı Örnek 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awal kita install program MS word garis tersebut tidak muncul. cara menampilkan ruler & garis batas margin atau text boundaries : 1. untuk ruler klik View pada toolbar lalu centang ruler...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/2376538/ff6dae326314269db86a1a03a1ef97a3/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/e01B5AEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"18","reqid":"1769649298363999-514366473176398324-balancer-l7leveler-kubr-yp-sas-15-BAL","summary":{"fullTextUrl":"/int_search_summary?data=http%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3D-1h_hUyrJ-E","linkTemplate":"/video/preview/11092987252359374679?parent-reqid=1769649298363999-514366473176398324-balancer-l7leveler-kubr-yp-sas-15-BAL&text=Marginal+Boundaries&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Cara menampilkan ruler & garis batas margin [text boundaries] | ms word 2010","related_orig_text":"Marginal 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