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Sınıf Olasılık Konusu Eğitim Videosu","beginTime":0}],"fullResult":[{"index":0,"title":"Olasılık Kavramları","list":{"type":"unordered","items":["Deney, farklı tekrarlarında farklı sonuçlar elde edilebilen ve tekrarlanabilen eylemlerdir (örneğin zar atma, rakam seçme, madeni para atma).","Çıktı, bir deneyin sonuçlarının her birine o deneye ait çıktı denir (örneğin zar atma deneyinde zarın üst yüzüne bir gelmesi veya madeni para atılmasında üst tura gelmesi).","Olay, örnek uzayın her bir alt kümesidir ve örnek uzay, oluşabilecek tüm çıktıların oluşturduğu kümedir."]},"beginTime":6,"endTime":85,"href":"/video/preview/3696117661402575423?parent-reqid=1774193260064497-16880676146140931025-balancer-l7leveler-kubr-yp-vla-85-BAL&text=7eis&t=6&ask_summarization=1"},{"index":1,"title":"Örnek Uzay ve Eleman Sayısı","list":{"type":"unordered","items":["İki madeni paranın atılması deneyinde oluşan çıktılar: yazı-yazı, yazı-tura, tura-yazı, tura-tura olup örnek uzayın eleman sayısı dörttür.","Üç 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Eş Olası Olaylar","list":{"type":"unordered","items":["Bir olayın tümleyeni ile A olayının tümleyeninin birleşimi örnek uzayı (evrensel küme) verir.","Eş olası olaylar, aynı örnek uzaya ait iki olayın eleman sayıları eşit olan olaylardır (örneğin zar yüzeyinde her bir sayıdan birer tane var).","Ayrık olaylar, aynı örnek uzaya ait farklı iki olayın kesişimi boş küme olan olaylardır."]},"beginTime":388,"endTime":672,"href":"/video/preview/3696117661402575423?parent-reqid=1774193260064497-16880676146140931025-balancer-l7leveler-kubr-yp-vla-85-BAL&text=7eis&t=388&ask_summarization=1"},{"index":4,"title":"Olasılık Problemleri","list":{"type":"unordered","items":["Baba, İpe, Karaca ve Serra'ya sırasıyla birer şeker veriyor; toplam dokuz şeker var ve her şeker farklı.","Üç şeker birlikte dağıtıldığında, olası durumlar 8×9×7=14.504 olur.","Üçünün de beyaz şeker alması durumunda, olası durumlar 4×3×2=24 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olasılığı 0'dır.","Kesin olay, örnek uzayına eşit olan olaydır ve gerçekleşme olasılığı 1'dir.","Bir olayın gerçekleşmeme olasılığı, olayın tümleyeni şeklinde gösterilir ve bir olayın gerçekleşme olasılığı ile gerçekleşmeme olasılığının toplamı 1'e eşittir."]},"beginTime":1011,"endTime":1064,"href":"/video/preview/3696117661402575423?parent-reqid=1774193260064497-16880676146140931025-balancer-l7leveler-kubr-yp-vla-85-BAL&text=7eis&t=1011&ask_summarization=1"},{"index":7,"title":"Olasılık Problemleri Çözümü","list":{"type":"unordered","items":["Ayrık olayların gerçekleşme olasılıkları toplamı 1'e eşittir.","Bir olayın gerçekleşmeme olasılığı, olayın tümleyeni ile aynıdır.","Eş olumlu ve ayrık olayların gerçekleşme olasılıkları toplamı 1'e 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Eğitmen, fonksiyonların değerlerini bulma, fonksiyon kurallarını belirleme, fonksiyonların toplamını hesaplama ve fonksiyonların özelliklerini kullanma gibi konuları detaylı şekilde açıklamaktadır. Video, birinci testin çözümüyle başlayıp, on birinci soruya kadar olan bir dizi fonksiyon sorusunun çözümünü içermektedir.","Videoda ayrıca faktöriyel hesaplamaları, f(x+2) ifadesinin f(x) cinsinden ifade edilmesi, f(a+1) - f(a-1) ifadesinin değeri ve f(x) + f(x üzeri n) = 2x(x üzeri n) eşitliğini kullanarak f(x) fonksiyonunun f(x) yönünden eşiti olan ifadeyi bulma gibi özel problemler de çözülmektedir. Her problem için detaylı çözüm yöntemleri ve matematiksel işlemler gösterilmektedir."]},"endTime":2302,"title":"On Föyün Fonksiyonlar Konusu Çözüm Videosu","beginTime":0}],"fullResult":[{"index":0,"title":"Fonksiyon Problemleri Çözümü","list":{"type":"unordered","items":["Birinci soruda f(x+2) = 5x+7 olduğuna göre f(3) değeri 12 olarak bulunuyor.","İkinci soruda fonksiyon makinesi tablosu verilmiş ve f(x) = ax+b kuralı kullanılarak b değeri 4 olarak hesaplanıyor.","Üçüncü soruda f(2^x) = 3x+1 fonksiyonunda f(4) değeri 6 olarak bulunuyor."]},"beginTime":1,"endTime":221,"href":"/video/preview/7604815542288750249?parent-reqid=1774193260064497-16880676146140931025-balancer-l7leveler-kubr-yp-vla-85-BAL&text=7eis&t=1&ask_summarization=1"},{"index":1,"title":"Fonksiyon Denklemleri","list":{"type":"unordered","items":["f(x-2) = 4x - f(x) denklemi verilmiş, f(5) = 11 ve f(1) = 3 olarak hesaplanıyor.","f(x) = 3x+7 fonksiyonunda f(x+2) fonksiyonunun kuralı f(x+2) = 3x+13 olarak bulunuyor.","f(x) = (x-1) + 3 fonksiyonunda f(1) = 2 ve f(6) = 17 olarak hesaplanıyor."]},"beginTime":221,"endTime":588,"href":"/video/preview/7604815542288750249?parent-reqid=1774193260064497-16880676146140931025-balancer-l7leveler-kubr-yp-vla-85-BAL&text=7eis&t=221&ask_summarization=1"},{"index":2,"title":"İkinci Test Soruları","list":{"type":"unordered","items":["f(2x+1) = x² - 3x + 1 fonksiyonunda f(7) - f(1) = 0 olarak bulunuyor."]},"beginTime":588,"endTime":664,"href":"/video/preview/7604815542288750249?parent-reqid=1774193260064497-16880676146140931025-balancer-l7leveler-kubr-yp-vla-85-BAL&text=7eis&t=588&ask_summarization=1"},{"index":3,"title":"Fonksiyon Problemleri","list":{"type":"unordered","items":["Fonksiyon problemlerinde, f(4) değerini bulmak için x yerine 1 yazılması gerektiği belirtiliyor.","f(32) değerini bulmak için x yerine -3 yazılması gerektiği gösteriliyor.","Fonksiyon probleminde hiç f değeri verilmemişse, x yerine 2 yazarak f(3) = 5 değerini bulabiliyoruz."]},"beginTime":672,"endTime":805,"href":"/video/preview/7604815542288750249?parent-reqid=1774193260064497-16880676146140931025-balancer-l7leveler-kubr-yp-vla-85-BAL&text=7eis&t=672&ask_summarization=1"},{"index":4,"title":"Fonksiyon Kuralı Bulma","list":{"type":"unordered","items":["Fonksiyonun kuralını bulmak için eşitliğin sağ tarafı düzenlenerek f(x²+x-2) = -2(x²+x-2) + 3 şeklinde ifade ediliyor.","Fonksiyonun kuralı, içine giren sayıyı -2 ile çarpıp 3 ekleyerek elde ediliyor.","f(2) değeri için a=2 yazarak f(2) = -4 + 3 = -1 olarak bulunuyor."]},"beginTime":805,"endTime":912,"href":"/video/preview/7604815542288750249?parent-reqid=1774193260064497-16880676146140931025-balancer-l7leveler-kubr-yp-vla-85-BAL&text=7eis&t=805&ask_summarization=1"},{"index":5,"title":"Fonksiyon Sayısı Hesaplama","list":{"type":"unordered","items":["A kümesi 4 elemanlı, B kümesi 6 elemanlı olduğunda A'dan B'ye tanımlanan farklı fonksiyon sayısı x olarak veriliyor.","x sayısı 6⁴ olarak hesaplanıyor ve asal çarpanlarına ayrıldığında 3⁴×2⁴ olarak bulunuyor.","Asal bölenlerinin toplamı 3+2=5 olarak hesaplanıyor."]},"beginTime":912,"endTime":963,"href":"/video/preview/7604815542288750249?parent-reqid=1774193260064497-16880676146140931025-balancer-l7leveler-kubr-yp-vla-85-BAL&text=7eis&t=912&ask_summarization=1"},{"index":6,"title":"Fonksiyon Değerleri","list":{"type":"unordered","items":["f(1) değeri verilmiş, f(13) değeri isteniyor ve küçük değer olan 2x-3 için x=5 yazarak f(7) = f(1) = 3 bulunuyor.","2x-9 değerini 7 yapmak için x=8 yazarak f(13) = f(7) + 4 = 14 olarak hesaplanıyor.","Fonksiyon problemlerinde x'in katsayısına dikkat edilmesi gerektiği vurgulanıyor."]},"beginTime":963,"endTime":1090,"href":"/video/preview/7604815542288750249?parent-reqid=1774193260064497-16880676146140931025-balancer-l7leveler-kubr-yp-vla-85-BAL&text=7eis&t=963&ask_summarization=1"},{"index":7,"title":"Fonksiyon Toplamı","list":{"type":"unordered","items":["f(a) + f(b) = f(a+b) + 10 eşitliği kullanılarak a+b = 1 olarak bulunuyor.","f(1) değeri için x=1 yazarak f(1) = 2+5 = 7 olarak hesaplanıyor.","f(3) değeri için x=1 yazarak f(3) = g(-1) = -9 olarak bulunuyor."]},"beginTime":1090,"endTime":1195,"href":"/video/preview/7604815542288750249?parent-reqid=1774193260064497-16880676146140931025-balancer-l7leveler-kubr-yp-vla-85-BAL&text=7eis&t=1090&ask_summarization=1"},{"index":8,"title":"Fonksiyon Özellikleri","list":{"type":"unordered","items":["f(x)×f(y) = f(x×y) eşitliği kullanılarak f(81) değeri hesaplanıyor.","f(81) = f(9×9) = f(9)² olarak bulunuyor.","f(9) = f(3+3) = f(3)×f(3) = f(3)² olduğu için f(81) = f(3)⁴ olarak hesaplanıyor."]},"beginTime":1195,"endTime":1291,"href":"/video/preview/7604815542288750249?parent-reqid=1774193260064497-16880676146140931025-balancer-l7leveler-kubr-yp-vla-85-BAL&text=7eis&t=1195&ask_summarization=1"},{"index":9,"title":"Fonksiyon Değerleri Hesaplama","list":{"type":"unordered","items":["f(x-1) + f(x+1) = 4x-1 eşitliği kullanılarak f(1) = -5 ve f(-1) = -1 değerleri veriliyor.","f(5) değeri için x=2 ve x=4 değerleri kullanılarak f(3) + f(5) = 7 bulunuyor.","f(3) değerleri yok edilerek f(5) = -3/5 olarak hesaplanıyor."]},"beginTime":1291,"endTime":1412,"href":"/video/preview/7604815542288750249?parent-reqid=1774193260064497-16880676146140931025-balancer-l7leveler-kubr-yp-vla-85-BAL&text=7eis&t=1291&ask_summarization=1"},{"index":10,"title":"Fonksiyon Problemleri Çözümü","list":{"type":"unordered","items":["Fonksiyon pozitif tam sayılardan reel sayılara tanımlı ve f(x) = (n+3)! / 2^(n+3) formülüyle verilmiş.","f(n+2) değerini bulmak için x yerine n+2 yazarak işlem yapılır ve sonuç 2/(n+5) olarak bulunur.","f(x+2)'nin f(x) cinsinden eşiti sorulduğunda, f(x+2) = 3x+8 formülü bulunur ve ortak olan 3x ifadesi kullanılarak f(x+2) = f(x)+6 olarak ifade edilir."]},"beginTime":1426,"endTime":1702,"href":"/video/preview/7604815542288750249?parent-reqid=1774193260064497-16880676146140931025-balancer-l7leveler-kubr-yp-vla-85-BAL&text=7eis&t=1426&ask_summarization=1"},{"index":11,"title":"Fonksiyon Denklemleri","list":{"type":"unordered","items":["f(x) = 2x+m fonksiyonunda f(a+1) - f(a-1) ifadesinin değeri 4 olarak bulunur.","f(1) = 2x² - 2x + f(x) - 4 denklemi için f(1) değerini bulmak için iki bilinmeyenli denklem sistemi kurularak f(1) = 5/4 olarak hesaplanır.","f(x) = (2+2x)/(x+1) fonksiyonunda f(2) değeri için fonksiyon içindeki ifadeyi a olarak tanımlayarak f(2) = 4 olarak bulunur."]},"beginTime":1702,"endTime":2140,"href":"/video/preview/7604815542288750249?parent-reqid=1774193260064497-16880676146140931025-balancer-l7leveler-kubr-yp-vla-85-BAL&text=7eis&t=1702&ask_summarization=1"},{"index":12,"title":"Fonksiyon Kombinasyonları","list":{"type":"unordered","items":["f(x) ve g(x) fonksiyonları verilmiş, g(1) değeri için f(3) = -1 bulunarak g(1) = 1 olarak hesaplanır.","f(x-2) + f(x) = f(x+2) denklemi kullanılarak f(2022) değeri için bir dizi oluşturulur.","Denklem sistemi taraf tarafa toplanarak f(2022) değeri hesaplanır ve 1'den 11'e kadar sayıların toplamı bulunur."]},"beginTime":2140,"endTime":2306,"href":"/video/preview/7604815542288750249?parent-reqid=1774193260064497-16880676146140931025-balancer-l7leveler-kubr-yp-vla-85-BAL&text=7eis&t=2140&ask_summarization=1"},{"index":13,"title":"Matematik Problemi Çözümü","list":{"type":"unordered","items":["Bir matematik problemi çözülüyor ve son terim olarak 11+12/2 hesaplanıyor, sonuç 132+133=265 olarak bulunuyor.","Son soruda n pozitif doğal sayı olmak üzere f(x+y)=f(x)+f(y) şeklinde bir fonksiyon tanımı veriliyor.","f(x^n) ifadesi için x^n ifadesi x ile x^(n-1) çarpımı şeklinde yazılıyor ve f(x^n)=f(x)+f(x^(n-1)) olarak hesaplanıyor."]},"beginTime":2318,"endTime":2394,"href":"/video/preview/7604815542288750249?parent-reqid=1774193260064497-16880676146140931025-balancer-l7leveler-kubr-yp-vla-85-BAL&text=7eis&t=2318&ask_summarization=1"},{"index":14,"title":"Fonksiyonun Genelleştirilmesi","list":{"type":"unordered","items":["x^(n-1) ifadesi n-1 tane x'in çarpımı olarak yazılıyor ve x^(n-2) ile x çarpımı şeklinde ifade ediliyor.","Bu işlem devam ederek f(x^n)=f(x)+f(x^(n-1))=f(x)+f(x^(n-2))+f(x^(n-3))+... şeklinde genelleştiriliyor.","x^n ifadesi n defa açıldığında n tane f(x) ortaya çıkıyor ve toplamları n*f(x) olarak hesaplanıyor, cevap C olarak belirleniyor."]},"beginTime":2394,"endTime":2507,"href":"/video/preview/7604815542288750249?parent-reqid=1774193260064497-16880676146140931025-balancer-l7leveler-kubr-yp-vla-85-BAL&text=7eis&t=2394&ask_summarization=1"}],"linkTemplate":"/video/preview/7604815542288750249?parent-reqid=1774193260064497-16880676146140931025-balancer-l7leveler-kubr-yp-vla-85-BAL&text=7eis&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"EİS 9 Mat DAF, 7.Föy (Kümeler 4) Ödev Testleri 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