{"id":26210,"date":"2023-12-07T02:27:34","date_gmt":"2023-12-07T02:27:34","guid":{"rendered":"https:\/\/masterskills.org\/blog\/dinh-luat-gioi-han-trung-tam-central-limit-theorem-clt-la-gi-clt-trong-tai-chinh.html"},"modified":"2023-12-22T11:29:40","modified_gmt":"2023-12-22T04:29:40","slug":"dinh-luat-gioi-han-trung-tam-central-limit-theorem-clt-la-gi-clt-trong-tai-chinh","status":"publish","type":"post","link":"https:\/\/masterskills.org\/blog\/dinh-luat-gioi-han-trung-tam-central-limit-theorem-clt-la-gi-clt-trong-tai-chinh.html","title":{"rendered":"\u0110\u1ecbnh lu\u1eadt gi\u1edbi h\u1ea1n trung t\u00e2m (Central Limit Theorem – CLT) l\u00e0 g\u00ec? CLT trong t\u00e0i ch\u00ednh"},"content":{"rendered":"
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Hi\u0300nh minh ho\u0323a. Ngu\u00f4\u0300n: Youtube.com<\/i><\/p>\n<\/div>\n<\/div>\n

\u0110\u1ecbnh lu\u1ead<\/span>t gi\u1edbi h\u1ea1n trung t\u00e2m<\/font><\/h2>\n

Kha\u0301i ni\u00ea\u0323m<\/b><\/p>\n

\u0110\u1ecbnh lu\u1ead<\/span>t gi\u1edbi h\u1ea1n trung t\u00e2m<\/b> trong ti\u00ea\u0301ng Anh la\u0300 Central Limit Theorem, <\/b>vi\u1ebft t\u1eaft l\u00e0\u00a0CLT<\/b>.<\/p>\n

Trong ca\u0301c l\u00ed<\/span> thuy\u1ebft x\u00e1c su\u1ea5t, \u0111\u1ecbnh lu\u1ead<\/span>t gi\u1edbi h\u1ea1n trung t\u00e2m (CLT)<\/b> cho r\u1eb1ng gia\u0301 tri\u0323 trung bi\u0300nh ph\u00e2n ph\u1ed1i m\u1eabu g\u1ea7n b\u1eb1ng v\u01a1\u0301i ph\u00e2n ph\u1ed1i chu\u1ea9n (c\u00f2n \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 ph\u00e2n ph\u00f4\u0301i \u0111\u01b0\u1eddng cong hi\u0300nh chu\u00f4ng) khi ki\u0301ch th\u01b0\u01a1\u0301c m\u00e2\u0303u ca\u0300ng l\u01a1\u0301n, gi\u1ea3 s\u1eed r\u1eb1ng t\u1ea5t c\u1ea3 c\u00e1c m\u1eabu \u0111\u1ec1u gi\u1ed1ng h\u1ec7t nhau \u01a1\u0309 k\u00edch th\u01b0\u1edbc v\u00e0 h\u00ecnh d\u1ea1ng ph\u00e2n b\u1ed1.<\/p>\n

N\u00f3i m\u1ed9t c\u00e1ch kh\u00e1c, CLT l\u00e0 m\u1ed9t li\u0301 thuy\u1ebft th\u1ed1ng k\u00ea cho r\u1eb1ng v\u1edbi c\u1ee1 m\u1eabu \u0111\u1ee7 l\u1edbn t\u1eeb m\u1ed9t t\u00f4\u0309ng th\u1ec3 c\u00f3 m\u1ee9c ph\u01b0\u01a1ng sai h\u1eefu h\u1ea1n, gi\u00e1 tr\u1ecb trung b\u00ecnh c\u1ee7a t\u1ea5t c\u1ea3 c\u00e1c m\u1eabu t\u1eeb c\u00f9ng t\u00f4\u0309ng th\u1ec3 \u0111o\u0301 s\u1ebd x\u1ea5p x\u1ec9 b\u1eb1ng gia\u0301 tri\u0323 trung b\u00ecnh c\u1ee7a t\u00f4\u0309ng th\u1ec3. H\u01a1n n\u1eefa, t\u1ea5t c\u1ea3 c\u00e1c m\u1eabu s\u1ebd tu\u00e2n theo m\u1ed9t m\u1eabu ph\u00e2n ph\u1ed1i g\u1ea7n v\u01a1\u0301i ph\u00e2n ph\u00f4\u0301i chu\u00e2\u0309n v\u1edbi t\u1ea5t c\u1ea3 c\u00e1c ph\u01b0\u01a1ng sai x\u1ea5p x\u1ec9 b\u1eb1ng ph\u01b0\u01a1ng sai c\u1ee7a t\u00f4\u0309ng th\u00ea\u0309 chia cho k\u00edch th\u01b0\u1edbc c\u1ee7a t\u01b0\u0300ng m\u1eabu.<\/p>\n

M\u1eb7c d\u00f9 kh\u00e1i ni\u1ec7m n\u00e0y \u0111\u01b0\u1ee3c gi\u01a1\u0301i thi\u1ec7u l\u1ea7n \u0111\u1ea7u ti\u00ean b\u1edfi Abraham de Moivre v\u00e0o n\u0103m 1733, n\u00f3 \u0111\u01b0\u1ee3c \u0111\u1eb7t t\u00ean ch\u00ednh th\u1ee9c l\u00e0 \u0110\u1ecbnh lu\u1ead<\/span>t gi\u1edbi h\u1ea1n trung t\u00e2m <\/b>va\u0300o n\u0103m 1930 b\u01a1\u0309i nh\u00e0 to\u00e1n h\u1ecdc ng\u01b0\u1eddi Hungary George Polya.<\/p>\n

Hi\u1ec3u v\u00ea\u0300 \u0111\u1ecbnh lu\u1ead<\/span>t\u00a0gi\u1edbi h\u1ea1n trung t\u00e2m\u00a0<\/font><\/h3>\n

Theo \u0111\u1ecbnh lu\u1ead<\/span>t\u00a0gi\u1edbi h\u1ea1n trung t\u00e2m<\/b>, gi\u00e1 tr\u1ecb trung b\u00ecnh c\u1ee7a m\u1ed9t m\u1eabu s\u1ebd g\u1ea7n v\u1edbi gi\u00e1 tr\u1ecb trung b\u00ecnh c\u1ee7a t\u00f4\u0309ng th\u00ea\u0309 n\u00f3i chung, khi k\u00edch th\u01b0\u1edbc m\u1eabu t\u0103ng l\u00ean b\u1ea5t ch\u1ea5p da\u0323ng ph\u00e2n ph\u1ed1i d\u1eef li\u1ec7u trong th\u1ef1c t\u1ebf. N\u00f3i c\u00e1ch kh\u00e1c, d\u1eef li\u1ec7u l\u00e0 ch\u00ednh x\u00e1c cho d\u00f9 ph\u00e2n ph\u1ed1i chu\u00e2\u0309n hay ph\u00e2n ph\u00f4\u0301i kha\u0301c.<\/p>\n

Theo nguy\u00ean t\u1eafc chung, k\u00edch th\u01b0\u1edbc m\u1eabu b\u1eb1ng ho\u1eb7c l\u1edbn h\u01a1n 30 \u0111\u01b0\u1ee3c coi l\u00e0 \u0111\u1ee7 \u0111\u1ec3 tu\u00e2n theo CLT<\/b>, c\u00f3 ngh\u0129a l\u00e0 ph\u00e2n ph\u1ed1i c\u1ee7a ca\u0301c gia\u0301 tri\u0323 trung bi\u0300nh m\u1eabu \u0111\u01b0\u1ee3c ph\u00e2n ph\u1ed1i kh\u00e1 chu\u00e2\u0309n. Do \u0111\u00f3, c\u00e0ng l\u1ea5y nhi\u1ec1u m\u1eabu, k\u1ebft qu\u1ea3 \u0111\u1ed3 th\u1ecb c\u00e0ng c\u00f3 h\u00ecnh d\u1ea1ng ph\u00e2n ph\u1ed1i chu\u00e2\u0309n.<\/p>\n

\u0110\u1ecbnh lu\u1ead<\/span>t gi\u1edbi h\u1ea1n trung t\u00e2m th\u1ec3 hi\u1ec7n m\u1ed9t hi\u1ec7n t\u01b0\u1ee3ng trong \u0111\u00f3 gia\u0301 tri\u0323 trung b\u00ecnh v\u00e0 \u0111\u1ed9 l\u1ec7ch chu\u1ea9n c\u1ee7a m\u1eabu b\u1eb1ng gia\u0301 tri\u0323 trung b\u00ecnh v\u00e0 \u0111\u1ed9 l\u1ec7ch chu\u1ea9n cu\u0309a t\u00f4\u0309ng th\u00ea\u0309, \u0111i\u00ea\u0300u na\u0300y c\u1ef1c k\u1ef3 h\u1eefu \u00edch trong vi\u1ec7c d\u1ef1 \u0111o\u00e1n c\u00e1c \u0111\u1eb7c \u0111i\u1ec3m c\u1ee7a t\u00f4\u0309ng th\u1ec3.<\/p>\n

\u0110\u1ecbnh lu\u1ead<\/span>t gi\u1edbi h\u1ea1n trung t\u00e2m trong t\u00e0i ch\u00ednh<\/font><\/h3>\n

CLT <\/b>r\u1ea5t h\u1eefu \u00edch khi ki\u1ec3m tra l\u1ee3i nhu\u1eadn c\u1ee7a m\u1ed9t c\u1ed5 phi\u1ebfu ri\u00eang l\u1ebb ho\u1eb7c c\u00e1c ch\u1ec9 s\u1ed1 r\u1ed9ng h\u01a1n, b\u1edfi v\u00ec qua\u0301 tri\u0300nh ph\u00e2n t\u00edch r\u1ea5t \u0111\u01a1n gi\u1ea3n va\u0300 s\u1ef1 d\u1ec5 d\u00e0ng \u0111\u00ea\u0309 thu th\u1ead<\/span>p ca\u0301c d\u1eef li\u1ec7u t\u00e0i ch\u00ednh c\u1ea7n thi\u1ebft. Do \u0111\u00f3, c\u00e1c nh\u00e0 \u0111\u1ea7u t\u01b0 thu\u1ed9c m\u1ecdi lo\u1ea1i h\u00ecnh d\u1ef1a v\u00e0o CLT \u0111\u1ec3 ph\u00e2n t\u00edch l\u1ee3i nhu\u1eadn c\u1ed5 phi\u1ebfu, x\u00e2y d\u1ef1ng danh m\u1ee5c \u0111\u1ea7u t\u01b0 hay qu\u1ea3n l\u00ed<\/span> r\u1ee7i ro.<\/p>\n

V\u00ed d\u1ee5, m\u1ed9t nh\u00e0 \u0111\u1ea7u t\u01b0 mu\u1ed1n ph\u00e2n t\u00edch l\u1ee3i nhu\u1eadn chung cho m\u1ed9t ch\u1ec9 s\u1ed1 ch\u1ee9ng kho\u00e1n bao g\u1ed3m 1.000 c\u1ed5 phi\u1ebfu. Trong tr\u01b0\u01a1\u0300ng h\u01a1\u0323p n\u00e0y, nh\u00e0 \u0111\u1ea7u t\u01b0 \u0111\u00f3 c\u00f3 th\u1ec3 ch\u1ec9 c\u1ea7n nghi\u00ean c\u1ee9u m\u1ed9t m\u1eabu c\u1ed5 phi\u1ebfu ng\u1eabu nhi\u00ean, \u0111\u1ec3 xa\u0301c \u0111i\u0323nh l\u1ee3i nhu\u1eadn \u01b0\u1edbc t\u00ednh c\u1ee7a toa\u0300n b\u1ed9 ch\u1ec9 s\u1ed1. Trong \u0111o\u0301 m\u00e2\u0303u pha\u0309i co\u0301 i\u0301t nh\u1ea5t 30 c\u1ed5 phi\u1ebfu pha\u0309i \u0111\u01b0\u1ee3c ch\u1ecdn ng\u1eabu nhi\u00ean v\u01a1\u0301i c\u00e1c l\u0129nh v\u1ef1c kh\u00e1c nhau, \u0111\u1ec3 CLT\u00a0co\u0301 th\u00ea\u0309 a\u0301p du\u0323ng \u0111\u01b0\u01a1\u0323c. Ngoa\u0300i ra, c\u00e1c c\u1ed5 phi\u1ebfu \u0111\u01b0\u1ee3c ch\u1ecdn tr\u01b0\u1edbc \u0111\u00f3 ph\u1ea3i \u0111\u01b0\u1ee3c ho\u00e1n \u0111\u1ed5i v\u1edbi c\u00e1c c\u00f4\u0309 phi\u00ea\u0301u kh\u00e1c \u0111\u1ec3 lo\u1ea1i b\u1ecf s\u1ef1 thi\u00ean v\u1ecb khi ph\u00e2n ti\u0301ch.<\/p>\n

Ca\u0301c y\u0301 chi\u0301nh<\/font><\/h3>\n

– \u0110\u1ecbnh lu\u1ead<\/span>t gi\u1edbi h\u1ea1n trung t\u00e2m (CLT)<\/b> cho r\u1eb1ng ph\u00e2n ph\u1ed1i cu\u0309a ca\u0301c gia\u0301 tri\u0323 trung bi\u0300nh m\u1eabu x\u1ea5p x\u1ec9 ph\u00e2n ph\u1ed1i chu\u1ea9n khi k\u00edch th\u01b0\u1edbc m\u1eabu ca\u0300ng l\u1edbn.<\/p>\n

– C\u1ee1 m\u1eabu b\u1eb1ng ho\u1eb7c l\u1edbn h\u01a1n 30 \u0111\u01b0\u1ee3c coi l\u00e0 \u0111\u1ee7 \u0111\u1ec3 a\u0301p du\u0323ng CLT.<\/p>\n

– M\u1ed9t kh\u00eda c\u1ea1nh quan tr\u1ecdng c\u1ee7a CLT l\u00e0 gia\u0301 tri\u0323 trung b\u00ecnh v\u00e0 \u0111\u1ed9 l\u1ec7ch chu\u1ea9n c\u1ee7a m\u1eabu s\u1ebd b\u1eb1ng gia\u0301 tri\u0323 trung b\u00ecnh v\u00e0 \u0111\u1ed9 l\u1ec7ch chu\u1ea9n cu\u0309a t\u00f4\u0309ng th\u00ea\u0309.<\/p>\n

– M\u1ed9t ki\u0301ch c\u1ee1 m\u1eabu \u0111\u1ee7 l\u1edbn c\u00f3 th\u1ec3 d\u1ef1 \u0111o\u00e1n ch\u00ednh x\u00e1c c\u00e1c \u0111\u1eb7c \u0111i\u1ec3m c\u1ee7a t\u00f4\u0309ng th\u00ea\u0309.<\/p>\n

(Theo Investopedia<\/i>)<\/p>\n<\/p><\/div>\n","protected":false},"excerpt":{"rendered":"

\n \u0110\u1ecbnh lu\u1eadt gi\u1edbi h\u1ea1n trung t\u00e2m (ti\u00ea\u0301ng Anh: Central Limit Theorem) l\u00e0 m\u1ed9t l\u00ed thuy\u1ebft th\u1ed1ng k\u00ea cho r\u1eb1ng v\u1edbi c\u1ee1 m\u1eabu \u0111\u1ee7 l\u1edbn t\u1eeb m\u1ed9t t\u00f4\u0309ng th\u1ec3 c\u00f3 ph\u01b0\u01a1ng sai h\u1eefu h\u1ea1n, gi\u00e1 tr\u1ecb trung b\u00ecnh c\u1ee7a t\u1ea5t c\u1ea3 c\u00e1c m\u1eabu s\u1ebd x\u1ea5p x\u1ec9 b\u1eb1ng trung b\u00ecnh c\u1ee7a t\u00f4\u0309ng th\u1ec3.\n <\/div>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[414],"tags":[],"_links":{"self":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/posts\/26210"}],"collection":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/comments?post=26210"}],"version-history":[{"count":0,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/posts\/26210\/revisions"}],"wp:attachment":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/media?parent=26210"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/categories?post=26210"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/tags?post=26210"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}