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강좌 개요 및 확률 모델 |
Course objective and outline, models and probabilistic models, typical examples of probabilistic models |
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2. |
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확률 이론의 기본 개념 I |
Axioms of probability, discrete and continuous sample spaces, counting methods, conditional probability |
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3. |
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확률 이론의 기본 개념 II |
Independence of events, sequence of independent experiments, sequence of dependent experiments, random number generators |
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4. |
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이산확률변수 I |
Definition of random variable, probability mass function (pmf), expected value of a random variable, variance of a random variable |
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5. |
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이산확률변수 II |
Conditional pmf, conditional expected value, important discrete random variables, generation of discrete random variables |
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6. |
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단일 확률변수 I |
Cumulative distribution function (cdf), types of random variables, probability density function (pdf), conditional cdf's and pdf's, expected value of function of a random variable |
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7. |
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단일 확률변수 II |
Variance and other parameters, important continuous random variables, function of a random variable |
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8. |
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단일 확률변수 III |
Useful inequalities, transform methods, generation of random variables |
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9. |
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다중 확률변수 I |
Two random variables, joint and marginal pmf, joint and marginal cdf, joint and marginal pdf |
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10. |
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다중 확률변수 II |
Independence of multiple random variables, joint moment, correlation and covariance, conditional probability |
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11. |
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다중 확률변수 III |
Conditional expectation, functions of multiple random variables, jointly Gaussian random variables |
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12. |
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확률변수의 합 |
Sums of random variables, pdf of sums of random variables, sample mean, law of large number, central limit theorem |
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13. |
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통계 입문 |
samples and sampling distributions, parameter estimation, properties of estimators, hypothesis testing |
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14. |
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확률과정 입문 |
Definition and interpretation of random process, categorization of random processes, specification of random process, stationary random process |
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