Á¦1Àå ÁÖ¿ä³»¿ë°ú
Áú¹®
1.1 Set Theory
- ¹«ÇÑ °³(countable or uncountable)ÀÇ ÁýÇÕ¿¡ ´ëÇÑ ÇÕÁýÇÕ°ú
±³ÁýÇÕÀÇ Á¤ÀÇ
- ºÐÇÒ(partition)
1.2 Probability Theory
- È®·üÀÇ °ø¸®Àû Á¤ÀÇ
- [Q](Question) Borel fieldÀÇ Á¤ÀÇ´Â ¿Ö ÇÊ¿äÇÑ°¡?
- [Q] ¿Ö È®·üÀ» °ø¸®ÀûÀ¸·Î Á¤ÀÇÇØ¾ß Çϴ°¡? (È®·üÀ» ´Ù¸£°Ô Á¤ÀÇÇÒ ¼ö Àִ°¡?)
- È®·üÀÇ ¼ºÁú: [Q] °ø¸®¿Í ¼ºÁúÀº ¾î¶»°Ô ´Ù¸¥°¡?
- Boole's inequality and Bonferroni's inequality: Theorem
1.2.11.b and equation (1.2.10)
- Áߺ¹Á¶ÇÕ(unordered-with-replacement case) °æ¿ìÀÇ ¼ö À¯µµ
°úÁ¤À» ÀÌÇØÇÏ°í °á°ú¸¦ ¾Ï±â
1.3 Conditional Probability and Independence
- Example 1.3.4
- [Q] '°£¼ö°¡ Á˼ö B´Â »çÇüÁýÇàµÈ´Ù°í ¸»ÇÒ' »ç°Ç°ú 'Á˼ö
B´Â »çÇüÁýÇàµÉ' »ç°ÇÀº °°Àº »ç°ÇÀΰ¡? ºñ½ÁÇÑ ´ÙÀ½ ¹®Á¦¸¦ »ý°¢ÇØ º¸ÀÚ: ¸¸¾à
±è¾¾°¡ µÎ Àڳฦ µÎ°í ÀÖ´Ù´Â °ÍÀ» ¾È´Ù°í ÇÏÀÚ. ÀÌ ¶§ 'µÎ ÀÚ³à Áß¿¡¼ Àû¾îµµ ¾ÆµéÀÌ ÇÑ ¸í ÀÖÀ»'
»ç°Ç(»ç°Ç A)°ú '±è¾¾ ÁýÀ» ¹æ¹®ÇßÀ»
¶§ ¾Æµé ÇÑ ¸íÀ» º¼' »ç°Ç(»ç°Ç B)Àº ¼·Î ´Ù¸¥ »ç°ÇÀÌ´Ù.
»ç°Ç B°¡ ÁÖ¾îÁö¸é »ç°Ç A°¡ ÀϾ È®·üÀº 1ÀÌÁö¸¸ »ç°Ç A°¡ ÁÖ¾îÁø´Ù°í Çؼ
»ç°Ç B°¡ ¹Ýµå½Ã ÀϾ´Â °ÍÀº ¾Æ´Ï´Ù.
- Bayes' rule
- µ¶¸³»ç°ÇÀÇ Á¤ÀÇ
1.4 Random Variables
- È®·üº¯¼öÀÇ Á¤ÀÇ
- induced probability (P¿Í PX
)
- [Q] È®·üº¯¼ö´Â ¿Ö ÇÊ¿äÇÑ°¡?
1.5 Distribution Functions
- ´©ÀûºÐÆ÷ÇÔ¼öÀÇ Á¤ÀÇ¿Í ¼ºÁú
- ´©ÀûºÐÆ÷ÇÔ¼ö(FX) ´Â È®·üº¯¼öÀÇ
ºÐÆ÷(PX)¸¦ °áÁ¤ÇÑ´Ù.
(Theorem 1.5.10)
1.6 Density and Mass Functions
- È®·ü¹ÐµµÇÔ¼öÀÇ Á¤ÀÇ¿Í ¼ºÁú
- absolute continuous function F(x)¿Í continuous function
F(x)ÀÇ ±¸º°
Á¦1Àå ¿¬½À¹®Á¦(¼÷Á¦)
1 12 14 19 24 27 35 38 39
47 49 51 52 53 54 55
<12¹ø ¹®Á¦ ÈùÆ®>
À» »óÈ£¹è¹Ý(pairwise disjoint)ÀÎ »ç°ÇÀ̶ó°í ÇÏÀÚ.
¶ó°í Á¤ÀÇÇϸé,
,
À̸ç,
ÀÌ´Ù.