확률과 통계의 이해

제1장 통계학이란 무엇인가? ······························· 1
1.1 통계학의 정의 ··················································· 1
1.2 통계학의 목표 ···················································· 2
1.3 자료의 종류와 변수 ·······································3
1.4 그래프에 의한 자료요약 ············································4
1.5 수치에 의한 자료요약 ··········································9
1.6 도수분포표에서의 자료의 요약 ··································15
1.7 이변량 범주형 자료의 요약 ······························16
1.8 이변량 양적 자료의 요약 ··········································18
연 습 문 제 ············································22

제2장 확 률 ···················································27
2.1 서론 ·········································27
2.2 사상의 확률 ··················································· 28
2.3 확률의 계산 ··················································· 31
2.4 사상과의 관계와 확률법칙 ····························32
2.5 조건부확률과 독립 ·······································38
2.6 베이즈정리(Bayes' Rule) ·······························43
2.7 경우의 수 ················································ 46
2.8 이항계수(Binomial Coefficient) ·································· 51
연 습 문 제 ············································53

제3장 확률분포 ······················································· 61
3.1 확률변수 ···············································61
3.2 이산확률변수와 확률분포 ··········································63
3.3 연속확률변수와 확률밀도함수 ································ 67
3.4 두 확률변수의 결합확률분포 ·······························72
3.5 조건부 확률분포와 독립성 ····························80
연 습 문 제 ··················································································································· 85

제4장 기댓값 ···················································· 91
4.1 확률변수의 기댓값 ·······································91
4.2 모멘트 ············································97
4.3 체비세프(Chebyshev) 정리 ····································104
4.4 확률변수들의 선형결합의 모멘트 ·································· 107
4.5 조건부 기댓값 ···································109
4.6 모멘트 생성 함수 ·······································112
연 습 문 제 ··················································································································· 117

제5장 이산확률변수의 확률분포 ·····································121
5.1 서 론 ············································121
5.2 균일분포 ················································121
5.3 베르누이 분포 ···································122
5.4 이항분포 ················································122
5.5 음이항분포와 기하분포 ···········································127
5.6 초기하분포 ···················································130
5.7 포아송분포 ···················································132
5.8 다항분포 ················································136
5.9 다변량 초기하분포 ·········································137
연 습 문 제 ················································································································· 138

제6장 연속확률변수의 확률분포 ·····································143
6.1 서론 ·········································· 143
6.2 균일분포 ················································143
6.3 감마분포 ················································144
6.4 지수분포 ················································147
6.5 카이제곱분포 ···················································149
6.6 베타분포 ················································151
6.7 정규분포 ················································154
6.8 이항분포의 정규근사와 연속성 수정 ······················158
6.9 이변량 정규분포 ······································161
연 습 문 제 ················································································································· 164

제7장 확률변수의 함수 ··············································169
7.1 서론 ·········································· 169
7.2 분포함수기법(distribution function technique) ·················170
7.3 변형기법(transformation technique) ····························174
7.4 모멘트 생성함수 기법 ············································179
연 습 문 제 ················································································································· 183

제8장 표본분포 ·······················································185
8.1 서론 ·········································· 185
8.2 표본평균의 표본분포와 중심극한정리 ·······················185
8.3 카이제곱분포 ···················································189
8.4 t분포 ·························································192
8.5 F분포 ··························································195
연 습 문 제 ················································································································· 198

제9장 통계적 추론 ············································201
9.1 서론 ············································ 201
9.2 점추정 ·············································201
9.3 구간추정 ················································207
연 습 문 제 ················································································································· 226

제10장 가설검정 ··············································231
10.1 서론 ············································231
10.2 검정절차 ··················································232
10.3 검정오류 ··················································235
10.4 모평균(μ)에 대한 가설검정(σ가 알려져 있지 않을 때) ··············236
10.5 모비율(p)에 대한 가설검정 ·······································244
10.6 모분산(σ )에 대한 가설검정 ·····································245
10.7 모평균의 차이(μ1 - μ2)에 대한 가설검정 ·························· 246
10.8 대응표본에서 모평균의 차(δ= μ1 - μ2)에 대한 가설검정 ········· 248
10.9 두 모비율 차이(p1 - p2)에 대한 가설검정 ·····················250
10.10 두 모분산의 비율()에 대한 가설검정 ························· 252
10.11 신뢰구간과 가설검정 ··········································· 253
연 습 문 제 ················································································································· 255

제11장 분산분석 ·················································261
11.1 서론 ·········································· 261
11.2 일요인 분산분석 ······································262
연 습 문 제 ················································································································· 270

제12장 회귀분석 ·················································273
12.1 서론 ·········································273
12.2 단순선형회귀모형 ·······································274
12.3 회귀계수추정 ···················································276
연 습 문 제 ················································································································· 280

부록 ····························································283

연습문제 해답 ·············································299