MATH 281 • Tüm Sınavlar • Probability
Bu ders ile MATH 281 sınavı için temel konseptleri çok iyi anlamakla kalmayıp sınava girmeye de tamamen hazır olacaksın.
Dersin içeriğinde yer alan Permutation, Combination, Binomial Theorem, Rules of Probability, Conditional Probability, Independence, Bayes Theorem, Random Variable, PDF, CDF, Expected Value, Variance, Binomial Distribution ve Poisson Distribution kavramlarını çok iyi öğreneceksin ve hepsine dair en az birer örnek soru göreceksin.
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Eğitmenler
Ömer Faruk Altun
Co-founder & Head of Education
2011 yılında Endüstri Mühendisliği okumak için başladığım Sabancı Üniversitesi'nden 2018 yılında Bilgisayar Mühendisi olarak mezun oldum. 13 yıldır Altun ismiyle başta Sabancı Üniversitesi olmak üzere çeşitli okullarda Endüstri ve Bilgisayar Mühendisliği alanlarında ders vermekteyim. Unicourse'ta sunduğum derslerin yanında eğitim departmanının da sorumluluğunu üstlenmekteyim.
İhsan Altundağ
Eğitmen
2007 yılında Galatasaray Üniversitesi Bilgisayar Mühendisliği bölümünden birincilikle mezun olduktan sonra Fransa'da Kriptoloji üzerine Fransa hükümeti tarafından verilen bursla yüksek lisans yaptım. Devamında ikinci kez sınava girerek Boğaziçi Matematik bölümünü de bitirdim. Yaklaşık 15 yıldır üniversite öğrencilerine dersler vermekteyim.
Konular
Counting
14 konu anlatımı
Basic Principles of Counting
Counting Examples
Permutations
Permutations Example
Groups and Circular Permutation Example
Identical Objects Example 1
Identical Objects Example 2
Identical Objects Example 3
Combination
n choose r
Committee Example 1
Committee Example 2
Ball Example 1
Ball Example 2
Axioms of Probability
11 konu anlatımı
Sample Space and Events
Probability
Axioms of Probability
Some Rules
Coin Example
Dice Example
Card Example 1
Card Example 2
Ball Example
Set Example
Birthday Example
Conditional Probability, Bayes' Rule and Independence
12 konu anlatımı
Conditioning Events
Total Probability Rule
Example 1
Example 2
Example 3
Example 4
Bayes' Rule
Bayes' Rule Example 1
Bayes' Rule Example 2
Independence
Independence Example 1
Independence Example 2
Sample Midterm Problems I
26 soru
Counting 1 - Product Rule
Counting 2 - Product Rule
Counting 3 - Product Rule
Counting 4 - Product Rule
Counting 5 - Permutations
Counting 6 - Permutations
Counting 7 - Permutations
Counting 8 - Permutations
Counting 9 - Permutations
Counting 10 - Permutations
Counting 11 - Circular Permutation
Counting 12 - Repeated Permutation
Counting 13 - Combinations
Axioms of Probability 1
Axioms of Probability 2
Axioms of Probability 3
Axioms of Probability 4
Conditional Probability and Independence 1
Conditional Probability and Independence 2
Conditional Probability and Independence 3
Conditional Probability and Independence 4
Bayes' Rule 1
Bayes' Rule 2
Bayes' Rule 3
Bayes' Rule 4
Bayes' Rule 5
Discrete Random Variables
12 konu anlatımı
Random Variables
Probability Mass Function
PMF Example 1
PMF Example 2
Cumulative Distribution Function
CDF Example 1
Expected Value
Expected Value Example 1
Expected Value Example 2
Variance
Variance Example 1
Variance Example 2
Special Discrete Distributions
18 konu anlatımı
Bernoulli Distribution Part 1
Bernoulli Distribution Part 2
Example 1
Example 2
Binomial Distribution Part 1
Binomial Distribution Part 2
Example 3
Example 4
Poisson Distribution Part 1
Poisson Distribution Part 2
Example 5
Example 6
Poisson Approximation to Binomial Distribution
Example 7
Geometric Distribution Part 1
Geometric Distribution Part 2
Example 8
Example 9
Sample Midterm Problems II
20 soru
Discrete Random Variables 1
Discrete Random Variables 2
Discrete Random Variables 3
Discrete Random Variables 4
Discrete Random Variables 5
Discrete Random Variables 6
Discrete Random Variables 7
Discrete Random Variables 8
Poisson Distribution 1
Poisson Distribution 2
Poisson Distribution 3
Binomial Distribution 1
Binomial Distribution 2
Binomial Distribution 3
Binomial Distribution 4
Poisson Approximation to Binomial 1
Poisson Approximation to Binomial 2
Geometric Distribution 1
Geometric Distribution 2
Geometric Distribution 3
Continuous Random Variables
9 konu anlatımı
Probability Density Function - PDF
Example 1
Cumulative Distribution Function - CDF
Example 2
Expected Value
Expected Value - Example 1
Expected Value - Example 2
Variance
Variance - Example 1
Special Continuous Probability Distributions: Continuous Uniform Distribution
3 konu anlatımı
Uniform Distribution
Example 1
Example 2
Sample Midterm Problems III
9 soru
Continuous Random Variables 1
Continuous Random Variables 2
Continuous Random Variables 3
Continuous Random Variables 4
Continuous Random Variables 5
Continuous Random Variables 6
Uniform Distribution 1
Uniform Distribution 2
Uniform Distribution 3
Special Continuous Distributions
16 konu anlatımı
Uniform Distribution
Example 1
Example 2
Exponential Distribution
Example 3
Example 4
Memoryless Property
Example 5
Normal Distribution
Standard Normal Distribution
Reading Z Table - Option 1
Reading Z Table - Option 2
Example 6
Gamma Distribution
Example 7
Relation of Gamma Distribution with Others
Discrete Joint Probability
6 konu anlatımı
Probability Mass Function
PMF Example
Marginal PMF and CDF
Expected Value
Variance
Expected Value and Variance Example
Sample Midterm Problems I
15 soru
Discrete Joint Distribution 1
Discrete Joint Distribution 2
Discrete Joint Probability 3
Discrete Joint Probability 4
Discrete Joint Distribution 5
Normal Distribution 1
Normal Distribution 2
Normal Distribution 3
Normal Distribution 4
Normal Distribution 5
Normal Distribution 6
Normal Distribution 7
Exponential Distribution 1
Exponential Distribution 2
Exponential Distribution 3
Continuous Joint Probability
3 konu anlatımı
Introduction
Marginal PDF and CDF
Expected Value and Variance
Chebyshev's Theorem, Random Sampling and Some Important Statistics
5 konu anlatımı
Chebyshev's Theorem
Example 1
Sample Mean
Sample Variance
Example 2
Data Analysis
6 konu anlatımı
Introduction
Measures of Central Tendancy
Example 1
Measures of Dispersion
Example 2
Example 3
Sampling Distribution - Central Limit Theorem
11 konu anlatımı
Central Limit Theorem - Z Distribution
Example 1
Example 2
Example 3
Example 4
Example 5
Normal Approximation to Binomial Distribution
Example 6
Reading T Table
T distribution
Example 6
Sample Final Problems II
17 soru
Continuous Joint Probability 1
Continuous Joint Probability 2
Continuous Joint Probability 3
Continuous Joint Probability 4
Continuous Joint Probability 5
Continuous Joint Probability 6
Continuous Joint Probability 7
Central Limit Theorem 1
Central Limit Theorem 2
Central Limit Theorem 3
Normal Approximation to Binomial 1
Normal Approximation to Binomial 2
Chebyshev's Theorem 1
Chebyshev's Theorem 2
Sample Mean and Variance 1
Sample Mean and Variance 2
T distribution
Classical Methods of Estimation - Point Estimation
5 konu anlatımı
Introduction
Unbiased Estimators 1
Unbiased Estimators 2
Efficient Estimators
Example
Classical Methods of Estimation - Interval Estimation
6 konu anlatımı · 1 soru
Table Values (SADECE Z ve T KISIMLARI DAHİL)
Confidence Interval of Mean (When variance is known)
Example 1
Exam Like Question 1
Confidence Interval of Mean (When variance is unknown)
Example 2
Example 3
Statistical Hypothesis
10 konu anlatımı · 1 soru
What are we doing?
Terminology
Example 1
Example 2
Exam Like Question 1
Testing Procedure
How to Perform the Test for Means
Example 1
Example 2
Example 3
Example 4
Sample Final Problems III
17 soru
Unbiased Estimator 1
Unbiased Estimator 2
Unbiased Estimator 3
Efficient Estimator
C.I. of Mean (Known Variance) 1
C.I. of Mean (Known Variance) 2
C.I. of Mean (Known Variance) 3
C.I. of Mean (Unknown Variance) 1
C.I. of Mean (Unknown Variance) 2
Statistical Hypothesis 1
Statistical Hypothesis 2
Statistical Hypothesis 3
Statistical Hypothesis 4
Statistical Hypothesis 5
Statistical Hypothesis 6
Statistical Hypothesis 7
Statistical Hypothesis 8