Posts

Continuous random variables

-
Image
Other Source Ringkasan Teori & Rumus Variabel Acak Kontinu 1. Definisi Variabel Acak Kontinu Variabel acak kontinu X dapat memiliki nilai apa pun dalam interval kontinu . Contoh: tinggi badan, waktu tunggu, suhu, laju peluruhan radioaktif. 2. Fungsi Kepadatan Peluang (PDF) Syarat PDF f(x) : 1. f(x) ≥ 0 untuk semua x 2. ∫ -∞ ∞ f(x) dx = 1 (total luas = 1) Grafik PDF f(x) x 3. Menghitung Peluang Karena P(X = a) = 0 , peluang hanya bisa dihitung untuk interval: P(a ≤ X ≤ b) = ∫ a b f(x) dx Untuk grafik sederhana bisa juga dengan geometri (luas segiempat, trapesium, segitiga). 4. Nilai Tengah (Median) Median m adalah nilai yang memenuhi: ∫ -∞ m f(x) dx = 0.5 Intuisi: letak vertikal yang membelah luas kurva menjadi dua bagian sama besar. 5. Persentil Umum Persentil- p (0 < p < 1) adalah q sedemikian hingga: ∫ -∞ q f(x) dx = p 6. Nilai Harapan (Mean) E(X) = μ = ∫ -∞ ∞ x f(x) dx 7. Varia...
Read more

Lines, Angles and Shapes

-
Image
Quiz 1: Fullscreen Mode Other Quiz Lines, Angles and Shapes - Theory and Formulas 3.1 Lines and Angles Types of Angles Angles can be classified based on their size: Type Size Example Acute angle Less than 90° 30°, 45°, 70° Right angle Exactly 90° Corner of a book Obtuse angle More than 90° but less than 180° 100°, 120°, 150° Reflex angle More than 180° but less than 360° 200°, 270°, 300° Special Pairs of Angles Complementary Angles: Two angles that add up to 90° . Supplementary Angles: Two angles that add up to 180° . Fundamental Angle Rules Angles on a Straight Line: The sum of angles on a straight line is 180° . ∑ ∠ on line = 180° Angles Around a Point: The sum of all angles around a single point is 360° . ∑ ...
Read more

Logarithmic And Exponential Functions

-
Image
Logarithmic & Exponential Functions All-in-One Theory Sheet 2.1 Logarithms to Base 10 Definition: If 10 x = y , then log 10 y = x (written log y for short). ┌-----┐ │ 10 │ │ ^ │ ← Exponent │ y │ └-----┘ log 1000 = 3 because 10³ = 1000 log 0.01 = –2 because 10 –2 = 0.01 2.2 Logarithms to Any Base a Definition: If a x = y with a > 0 and a ≠ 1 , then log a y = x . log₂ 32 = 5 because 2⁵ = 32 log₅ 1 = 0 because 5⁰ = 1 2.3 The Three Laws of Logarithms ┌-------┐ │ Laws │ └-------┘ Product: log a (xy) = log a x + log a y Quotient: log a (x / y) = log a x – log a y Power: log a (x n ) = n log a x 2.4 Solving Logarithmic Equations Golden Rule: Logs only exist for positive numbers. Use the laws to get a single log on each side. Drop the log...
Read more

Electrical Quantities

-
Image
Quiz 1:   Fullscreen Mode Chapter 16: Electrical Quantities – Theory and Formulas 16.1 Electric Charge Atoms contain: Protons – Positive charge Neutrons – No charge Electrons – Negative charge An atom is neutral when it has equal numbers of protons and electrons. Charging by Friction Electrons transfer from one material to another. The material that loses electrons becomes positively charged, and the one that gains electrons becomes negatively charged. Interaction of Charges Like charges repel Unlike charges attract Conductors and Insulators Conductors : Allow electrons to move freely (e.g., metals) Insulators : Hold electrons tightly (e.g., plastic, glass) 16.2 Electric Field An electric field is a region where a charge experiences a force. Field Line Directions Positive charge : Field lines point away Negative charge : Field lines point toward Field Strength Stronger where field lines are closer together. ...
Read more

Scientific Notation

-
Image
Scientific Notation Quiz Scientific Notation By Mr Agus Salim Score: 0 / 100 Question 1 of 20 Convert the following number to scientific notation: 23500 Answer in format: a.bc × 10^n Enter each digit and exponent separately below: First digit (a): Second digit (b): Third digit (c): ...
Read more