• Terminology
  • Experiment 실험
  • Sample space 표본 공간: 모든 결과의 집합
  • event 사건: 표본공간의 부분집합
  • Probability P(E) = |E| / |S|
    • 0≤P≤1
    • SUM P = 1
  • complementary event 여사건 P(E bar) = 1 - P(E)
  • conditional probability 조건부확률 P(E|F) = P(E ∩ F) / P(F)
  • independence 독립 P(E ∩ F) = P(E)P(F) P(E|F) = P(E)
  • Bernoulli trial 두가지 결과만 존재(success, fail) n번의 Bernoulli trial에서 k번의 success: nCk p^k q^n-k
  • random variable sample space → Real number의 함수 예) 동전 3번 던져서 2번 앞면: X = 2
• E, V
  • Expected value = expectation = mean = 평균 E(X) = SIGMA(P(s)X(s))
    • in bernoulli trial E(X) = np
    • E(aX+b) = aE(X)+b
    • E(XY) = E(X)E(Y) : X, Y is independent
  • Variance 분산
    • Deviation of X at S 편차 X(S) - E(X)
    • 분산 = 편차 제곱의 평균 V(X) = SIGMA( X(s) - E(X))^2 P(s)
    • Standard deviation 표준편차 sigma(X) = sqrt(V(X))
    • V(X) = E(X^2) - (E(X))^2
    • V(X) = E((X-E(X))^2)
    • in bernoulli trial V(X) = pq