เอกสารประกอบการเรียน การวิเคราะห์ข้อมูลทางรัฐศาสตร์ บทที่ ๒

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<p> 216 </p> <p>1</p> <p> 2 2.1 P(A) = A 0 1 2.1.1 (Sample (Sample point)</p> <p>space) S </p> <p> 1 1 1 </p> <p> 1 1 2 3 6 = S : {1,2,3,4,5,6} 6 I, I = 1,2,,6 2 2 </p> <p> S : {, , , } 2 </p> <p> 216 </p> <p>2</p> <p>{0,1,2}</p> <p> S : 0 2 </p> <p>1 1 1</p> <p>2 2 2 (Event) </p> <p> 2.1.2</p> <p> 1 1 (Compound Event)</p> <p> (Sample Event) </p> <p> 3 1 3</p> <p> A 1 3 A : { 3} A : {4,5,6}</p> <p> 4 2 1 B : 1 2 B : {,,} 1-4 </p> <p> 216 </p> <p>3</p> <p> 1. 1 </p> <p> (sample space) S = {1,2,3,4,5,6}</p> <p> (event) A : 3 A : {4,5,6} C : 1 C : {,,} </p> <p>2. S = {,, 2 ,}</p> <p> (A) = A</p> <p>P(A)</p> <p>P (B) = 1 = 3/4 P (C) = 1 = 2/4</p> <p>= P ( 3) = 3/6</p> <p> 216 </p> <p>4</p> <p>2.2 2.2.1 (Multiplications Rule) 2 1 = mn m 2 n </p> <p> 5 . . 4 . . . . 4 . . 5 1 2 3 4 5</p> <p> . . 5 . </p> <p> 1 . 2 3 4 .</p> <p> .</p> <p> 216 </p> <p>5</p> <p> 2.1 . . . 4x5 = 20 </p> <p> 216 </p> <p>6</p> <p> 6 5 6 5x6 = 30 7 0,1,2,3,4,5,6,7,8,9 . 4 . . 7,000 . 2</p> <p> 4 4 10 ( 0-9) 10 ( 0-9) 10 ( 0-9) 9 ( 0) (. , . . ) 2.2.2 (Permutation) = 9x10x10x10 = 9,000 </p> <p>. 4 </p> <p> (Factorial) n! 1 n n! = n(n-1)(n-2)1</p> <p> 216 </p> <p>7</p> <p> : k n (k 0 P(A) &gt; P(B)</p> <p>= P(B) + P(AB )</p> <p>= B (AB )</p> <p> 17 1 1 A B 3 P(AB) P(AB)</p> <p> AB 3 3 A : {2,4,6} B : {1,2,3} S : {1,2,3,4,5,6} AB AB = {1,2,3,4,6} = {5}</p> <p>P(AB) A B =1/6 P (AB) = P(A) + P(B) P(AB) = 3/6 + 3/6 - 1/6 = 5/6</p> <p> P (AB) (1/6) + (1/6) = 5/6</p> <p>= P(1) + P(2) + P(3) + P(4) + P(6) = (1/6) + (1/6) + (1/6) +</p> <p> 216 </p> <p>20</p> <p> (AND) (OR)1.</p> <p> A B A B P(A or B) = P(A) + P(B) P(A and B) P (AB) P (AB) P(AB) P(AB) = = P(A) + P(B) P(AB) A B = P(A) + P(B) </p> <p>2.</p> <p>P(A) + P(B) - P (AB)</p> <p>P(A and B) = P(A) + P(B) P(A or B) P(AB) =</p> <p> A B </p> <p> 18 10</p> <p> (A,B,C,D,E,F,G,H,I,J) 3 10 1. 3 10 2.</p> <p> XX 2 XX 1 </p> <p>( 10 ) 3.</p> <p> . XX 1 </p> <p> ) 10!2)</p> <p> 3 10 = 10C3 = 3!(10-3)! = 1/120 = 120 </p> <p> 216 </p> <p>21</p> <p> A : XX 1 2C1 = 2 </p> <p> 1 2 XX = 2 8 = 8C2 = 28 8C2 = 2 x 28 = 56 P(A) = 56/1203)</p> <p> XX 1 = 2C1 x = 0.4667</p> <p> XX F G</p> <p> B : XX 1 A : XX 1 C : XX 2 </p> <p> . P(A) = 0.4667</p> <p> C : = 2C2 = 1 8C1 = 8 </p> <p>XX 2 2 XX 1 8 = P(C) = 1C1 x 8C1/ 10C3 = (1 x 8)/120 = 8/120 P(AC) = B P(B) = AC</p> <p>AC = A C </p> <p>= P(AC) = P(A) + P(C) P(AC) = 56/120 + 8/120 - 0</p> <p> 216 </p> <p>22</p> <p>= 0.4667 + 0.0666</p> <p>= 0.5333</p> <p>2.6 </p> <p> 2 A : B : P(AB) = A </p> <p> 2 </p> <p> B B P(A B ) = A B A B </p> <p> B A P(A B) &gt; P(A B )</p> <p> B 2.6.1 A B P(AB)</p> <p> A B P(A B) P(A B) =</p> <p> 216 </p> <p>23</p> <p> 2.6.2 A B P(A B) = P(A) P(A B) = P(B) A B P(A B) = P(AB) A B P(A) P(A B) = P(B) A B A B P(A B) = P(A)</p> <p>P(B)</p> <p> 19 A B . P (AB) = 0.65, P(A) = 0.3, P(B) = 0.5 . P (AB) = 0.6, P(A) = 0.2, P(B) = 0.4</p> <p> ) P (AB) P(AB)</p> <p>= P(A) + P(B) - P(AB)</p> <p> = 0.3 +</p> <p>0.5 - 0.65 = 0.15 0 A B P(A B) = P(AB) / P(B) = 0.15/0.5 = 0.3 = P(A) P(A B) B A B =</p> <p>= P(A) + P(B) - P (AB)</p> <p>P(A) A </p> <p> 216 </p> <p>24</p> <p> 0.6 = 0</p> <p>) P(AB)</p> <p>= P(A) + P(B) - P (AB)</p> <p>= 0.2 + 0.4</p> <p> A B P(A B) =</p> <p> P(A)</p> <p>P(AB) / P(B) = 0/0.4 = 0 </p> <p> A B 1. A B A B P(AB) = P(A) x P(B) P(A1, A2,An) = P(A1) xP(A2/A1)xP(A3/ A1,A2)P(Aa/Aa A1, A2,An P(A1, A2,An) = P(AB) = P(A) x P(B/A)</p> <p> A B </p> <p>2. A1, A2,An Aa-2A2A1)</p> <p>1</p> <p>P(A1)xP(A)xxP(An)</p> <p> 20 12 3 2 1 2 1 </p> <p>1. 2. 3.</p> <p> 1 G1 : i ; i = 1,2 </p> <p>) 2 </p> <p> 216 </p> <p>25</p> <p>P(G1)</p> <p>D1 ; i ; i = 1,2 = 8/11 = 3/11 = 9/12 P(D1) P(G2/ D1) P(D2/ D1) = 9/11 = 2/11 = 3/12</p> <p>P(G2/ G1) P(D2/ G1)</p> <p> G1 D2 D1 G2 </p> <p>D1 G2) D1)</p> <p>P( 1 ) = P G1 D2) + P = P(G1)P(D2/ G1) + P(D1)P(G2/ = (9/12)(3/11) + (3/12)(3/11)</p> <p>= (9/22)</p> <p> 2 3 1 </p> <p>9 </p> <p> 1 =</p> <p>P( 1 1 ) (9/22)</p> <p>= 3C1 x 9C1 12C2</p> <p>) 2 3 2 </p> <p> 216 </p> <p>26</p> <p>9 </p> <p> 0 = (1/22)</p> <p>P( 2 ) = 3C2 9C0 ) 1 3 9 </p> <p>12C2</p> <p> 1 2 0 1 </p> <p>) + P( 2 ) 1</p> <p>P( 1 ) = P( 1 =</p> <p> P( 0 ) + P( 1 ) + P( 2 ) P( 1 ) + P( 2 ) = 1</p> <p>= 1 P( 0 ) 3C0 9C2 12C2</p> <p>= 1- 6/11 = 5/11</p> <p> A B 1. A B 2. A B</p> <p>3. A B 1. P(AB ) = P(A)P(B )</p> <p> 216 </p> <p>27</p> <p>P(B / A)</p> <p> A B P(B/A) P(B)] P(AB )</p> <p>P(AB )</p> <p>P(A)</p> <p>= P(AB ) = P(A)P(B / A)</p> <p>= P(A)[1-P(B/A) = P(A)[1-</p> <p>= P(B)</p> <p>2. P(AB )</p> <p>= P(A)P(B ) = P(B)P(A /B) = P(B)P(A )</p> <p>= P(B)[1-P(A/B)] A</p> <p>= P(B)[1-P(A)]</p> <p>3. P(A B ) A</p> <p> B </p> <p> B A</p> <p>= P(A )[1-P(B/ A )] = P(A )[1-P(B)] = P(A ) P(B )</p> <p>= P(A )P(B / A )</p> <p> n (C1, C2, ,Cn) S</p> <p> B</p> <p> U Ci = S CiCj = S </p> <p> ; i j = 1,2,,n A </p> <p> 216 </p> <p>28</p> <p> A P(Ci/A) =</p> <p>P(A)</p> <p>0 Cj </p> <p>P(A/Ci)P(Ci)</p> <p>P(A/Ci)P(Ci)</p> <p> C1, C2, ,Cn (CiA)(CjA) = ; i j</p> <p> P(A) = P(C1A) + P(C2A) ++P(CnA) P(A) = P(A/Ci)P(Ci) P(Cj/A) =</p> <p>A = (C1A) (C2A) (CnA)</p> <p>P(A/C1)P(C1) + P(A/C2)P(C2) ++ P(A/Cn)P(Cn) = P(C1A)</p> <p> P(Cj/A) =</p> <p>P(A/Cj)P(Cj) ..(1) P(A/Ci)P(Ci)</p> <p>P(A)</p> <p> Cj A (prior probability) P(Cj/A) (posterior probability)</p> <p> (1) </p> <p>(P(Cj/A)) P(Cj) P(Cj) </p> <p> 216 </p> <p>29</p> <p> 21 . 5 30% . 20% . 2 45% 2 2 1. .</p> <p> A1 : .</p> <p>2. A2 : </p> <p>R : 2 R : </p> <p> 2 </p> <p>A1 R A2</p> <p> P(A1) P(R/ A1) P(R / A1) P(R /A2)</p> <p>= 0.3 = 0.20</p> <p>P(A2) = 1-P(A1) = 0.7 P(R/A2) = 0.45 = 1-0.2 = 0.8</p> <p>= 1- P(R/ A1) = 1- P(R/A2)</p> <p>= 1-0.45 = 0.55</p> <p> 216 </p> <p>30</p> <p>(1) A1 A2</p> <p>(2) P(A) 0.3 0.7</p> <p>P(R/Ai) P(Ai)P(R/ Ai) = P(Ai R) 0.06 0.2 0.45 (0.2)(0.3) = (0.7)(0.45) = 0.315 P(R) = 0.375</p> <p>(3)</p> <p>(4)</p> <p>P(Ai /R) = (4)/(4) 0.16 0.06/0.375 = 0.315/0.375 = 0.84 1.0</p> <p>(5)</p> <p>1)</p> <p>P( ./ 2 = P(A1/R) P(A1/R) = P(A1/R) P(R) R = A1 RA2R</p> <p>A2R </p> <p>P(R) = P(A1 R) + P(A2R) A1 R P(R/ A1) = P(A1 R)</p> <p>P(Ai) P(A2)</p> <p>P(A1 R) = P(R)</p> <p>P(A1 R) = P(R/ A2) P(A2)</p> <p>P(R/ A1) P(A1) + P(R/ A2)</p> <p>= P(R/ A1) P(A1)</p> <p>0.06 + 0.315 = 0.375</p> <p>= (0.2)(0.3) + (0.7)(0.45) = = 0.06/0.375 = 0.16</p> <p>P(A/R)</p> <p> 216 2)</p> <p>31</p> <p>P(/ 2 ) = P(A2/R) P(A2/R) = P(A2R) = P(R/ A1) P(A1) P(R)</p> <p>(0.45)(0.7) = 0.84 0.375</p> <p>=</p> <p>0.375</p> <p> 216 </p> <p>32</p> <p> (Random Variable) 1. (Random Variable) () 1.1 (Discrete Random Variable)</p> <p>2. </p> <p> X X X X X X 145-180 145 X 180 3. (Probability Distribution) 1.2 (Continuous Random Variable)</p> <p> X X S 3.1 </p> <p> 2 X X </p> <p>X1, X2,,Xn X = x X P(x) = P[X=x] 1. 2.</p> <p>0 P(X=x) = P(x) 1</p> <p> P(X=x) = 1 P(x) = 1</p> <p> 216 3.</p> <p>33</p> <p>P(A) = P(X=x) A S</p> <p> = S =</p> <p> 1 4</p> <p>{0,1,2,3,4} 30 X () = 0 1 8 8/30 = 0.27 2 4 4/30 = 0.13 3 4 4/30 = 0.13 12 12/30 = 0.4</p> <p>4 2</p> <p>2/30 = 0.07</p> <p> 216 </p> <p>34</p> <p> P(2) = P(X = 2) = 0.13 P(0) = P(X = 0) = 0.4 P(3) = P(X = 3) = 0.132.</p> <p>P(1) = P(X = 1) = 0.27 P(4) = P(X = 4) = 0.07</p> <p>1. 2 </p> <p> 1 . A : 2 A : {2,3,4}</p> <p>0.13+0.13+0.07 = 0.33</p> <p> P(A) = P(X = 2) + P(X = 3) + P(X = 4)</p> <p>=</p> <p>. B : 1 B = {1,2,3,4} </p> <p>4)</p> <p>= 1- P(X = 0) = 1-0.4 = 0.6 3.2 </p> <p>P(B) = P(X = 1) + P(X = 2) + P(X = 3) + P(X =</p> <p> X X </p> <p> X </p> <p> X X [a,b], a b X [a,b] P[X = a] = 0 X </p> <p> 216 </p> <p>35</p> <p> X P[X</p>

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