{"id":25341,"date":"2023-12-07T00:21:50","date_gmt":"2023-12-07T00:21:50","guid":{"rendered":"https:\/\/masterskills.org\/blog\/qui-luat-so-lon-law-of-large-numbers-la-gi-noi-dung-cua-qui-luat-so-lon.html"},"modified":"2023-12-22T10:33:21","modified_gmt":"2023-12-22T03:33:21","slug":"qui-luat-so-lon-law-of-large-numbers-la-gi-noi-dung-cua-qui-luat-so-lon","status":"publish","type":"post","link":"https:\/\/masterskills.org\/blog\/qui-luat-so-lon-law-of-large-numbers-la-gi-noi-dung-cua-qui-luat-so-lon.html","title":{"rendered":"Qui lu\u1eadt s\u1ed1 l\u1edbn (Law of large numbers) l\u00e0 g\u00ec? N\u1ed9i dung c\u1ee7a qui lu\u1eadt s\u1ed1 l\u1edbn"},"content":{"rendered":"
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H\u00ecnh minh h\u1ecda<\/p>\n<\/div>\n<\/div>\n

Qui lu\u1eadt s\u1ed1 l\u1edbn (Law of large numbers)<\/font><\/h2>\n

\u0110\u1ecbnh ngh\u0129a<\/b><\/p>\n

Qui lu\u1eadt s\u1ed1 l\u1edbn<\/b> trong ti\u1ebfng Anh l\u00e0 L<\/b>aw of large numbers<\/b>.<\/i><\/p>\n

Qui lu\u1eadt s\u1ed1 l\u1edbn <\/i>l\u00e0\u00a0qui lu\u1eadt kinh t\u1ebf\u00a0cho r\u1eb1ng c\u00e1c\u00a0nh\u00f3m l\u1edbn th\u01b0\u1eddng c\u00f3 h\u00e0nh vi th\u1ed1ng nh\u1ea5t h\u01a1n l\u00e0 t\u1eebng c\u00e1 nh\u00e2n \u0111\u01a1n l\u1ebb.\u00a0Ch\u1eb3ng h\u1ea1n, m\u1ed9t ng\u01b0\u1eddi ti\u00eau d\u00f9ng n\u00e0o \u0111\u00f3 c\u00f3 th\u1ec3 mua nhi\u1ec1u h\u00e0ng h\u01a1n khi gi\u00e1 t\u0103ng nh\u01b0ng s\u1ed1 \u0111\u00f4ng s\u1ebd mua \u00edt h\u01a1n.<\/p>\n

Qui lu\u1eadt s\u1ed1 l\u1edbn<\/i> theo x\u00e1c su\u1ea5t v\u00e0 th\u1ed1ng k\u00ea cho r\u1eb1ng khi k\u00edch th\u01b0\u1edbc m\u1eabu t\u0103ng l\u00ean, gi\u00e1 tr\u1ecb trung b\u00ecnh c\u1ee7a n\u00f3 s\u1ebd g\u1ea7n v\u1edbi m\u1ee9c trung b\u00ecnh c\u1ee7a to\u00e0n b\u1ed9 t\u1ed5ng th\u1ec3.<\/p>\n

V\u00e0o th\u1ebf\u00a0k\u1ec9\u00a016, nh\u00e0 to\u00e1n h\u1ecdc Gerolama Cardano \u0111\u00e3 c\u00f4ng nh\u1eadn Qui lu\u1eadt s\u1ed1 l\u1edbn nh\u01b0ng ch\u01b0a bao gi\u1edd ch\u1ee9ng minh \u0111i\u1ec1u \u0111\u00f3.<\/p>\n

N\u0103m 1713, nh\u00e0 to\u00e1n h\u1ecdc ng\u01b0\u1eddi Th\u1ee5y S\u0129 Jakob Bernoulli \u0111\u00e3 ch\u1ee9ng minh Qui lu\u1eadt n\u00e0y trong cu\u1ed1n s\u00e1ch c\u1ee7a m\u00ecnh, Ars Conjectandi. Sau \u0111\u00f3, Qui lu\u1eadt s\u1ed1 l\u1edbn \u0111\u00e3 \u0111\u01b0\u1ee3c tinh ch\u1ec9nh b\u1edfi c\u00e1c nh\u00e0 to\u00e1n h\u1ecdc n\u1ed5i ti\u1ebfng kh\u00e1c, ch\u1eb3ng h\u1ea1n nh\u01b0 Pafnuty Ch Quashev, ng\u01b0\u1eddi s\u00e1ng l\u1eadp tr\u01b0\u1eddng ph\u00e1i to\u00e1n h\u1ecdc St. Petersburg.<\/p>\n

N\u1ed9i dung c\u1ee7a qui lu\u1eadt s\u1ed1 l\u1edbn trong x\u00e1c su\u1ea5t th\u1ed1ng k\u00ea<\/font><\/h3>\n

– Trong\u00a0x\u00e1c su\u1ea5t th\u1ed1ng k\u00ea,\u00a0Qui lu\u1eadt s\u1ed1 l\u1edbn<\/strong>\u00a0ch\u1ee9ng minh\u00a0s\u1ef1 \u1ed5n \u0111\u1ecbnh l\u00e2u d\u00e0i c\u1ee7a m\u1ed9t bi\u1ebfn ng\u1eabu nhi\u00ean. Cho v\u00ed d\u1ee5 v\u1ec1 c\u00e1c bi\u1ebfn ng\u1eabu nhi\u00ean \u0111\u1ed9c l\u1eadp ph\u00e2n b\u1ed1 \u0111\u1ec1u nhau v\u1edbi gi\u00e1 tr\u1ecb k\u00ec v\u1ecdng gi\u1edbi h\u1ea1n v\u00e0 ph\u01b0\u01a1ng sai, th\u00ec gi\u00e1 tr\u1ecb trung b\u00ecnh c\u1ee7a c\u00e1c quan s\u00e1t s\u1ebd d\u1ea7n d\u1ea7n ti\u1ebfn g\u1ea7n \u0111\u1ebfn gi\u00e1 tr\u1ecb k\u00ec v\u1ecdng khi s\u1ed1 l\u1ea7n quan s\u00e1t t\u0103ng l\u00ean.<\/p>\n

– Lu\u1eadt s\u1ed1 l\u1edbn c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c minh ho\u1ea1 d\u1ec5 d\u00e0ng qua vi\u1ec7c tung m\u1ed9t con x\u00fac x\u1eafc. Trong \u0111\u00f3, k\u1ebft qu\u1ea3 c\u1ee7a x\u00e1c su\u1ea5t xu\u1ea5t hi\u1ec7n c\u00e1c m\u1eb7t c\u00f3 1, 2, 3, 4, 5 v\u00e0 6 ch\u1ea5m l\u00e0 nh\u01b0 nhau. Gi\u00e1 tr\u1ecb k\u00ec v\u1ecdng c\u1ee7a c\u00e1c k\u1ebft qu\u1ea3 l\u00e0:<\/p>\n

(1 + 2 + 3 + 4 + 5 + 6) \/ 6 = 3,5<\/p>\n

C\u00e1c nh\u00e0 to\u00e1n h\u1ecdc ph\u00e2n bi\u1ec7t hai ph\u00e1t bi\u1ec3u kh\u00e1c nhau c\u1ee7a qui lu\u1eadt s\u1ed1 l\u1edbn, l\u00e0 qui lu\u1eadt s\u1ed1 l\u1edbn y\u1ebfu v\u00e0 qui lu\u1eadt s\u1ed1 l\u1edbn m\u1ea1nh.<\/p>\n

Qui lu\u1eadt s\u1ed1 l\u1edbn d\u1ea1ng y\u1ebfu<\/font><\/h3>\n

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X\u00e9t\u00a0n\u00a0bi\u1ebfn ng\u1eabu nhi\u00ean X1<\/sub>, X2<\/sub>, …, Xn<\/sub> l\u00e0 c\u00e1c bi\u1ebfn ng\u1eabu nhi\u00ean \u0111\u1ed9c l\u1eadp v\u1edbi nhau c\u00f3 c\u00f9ng ph\u00e2n ph\u1ed1i x\u00e1c su\u1ea5t v\u1edbi k\u00ec v\u1ecdng E(X)\u00a0lu\u1eadt s\u1ed1 l\u1edbn y\u1ebfu ph\u00e1t bi\u1ec3u r\u1eb1ng, v\u1edbi m\u1ecdi s\u1ed1 th\u1ef1c d\u01b0\u01a1ng, x\u00e1c su\u1ea5t \u0111\u1ec3 kho\u1ea3ng c\u00e1ch gi\u1eefa trung b\u00ecnh t\u00edch l\u0169y Yn<\/sub> v\u00e0 k\u00ec v\u1ecdng E(X) l\u1edbn h\u01a1n l\u00e0 ti\u1ebfn v\u1ec1 0 khi n ti\u1ebfn v\u1ec1 v\u00f4 c\u1ef1c.<\/p>\n

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Qui lu\u1eadt s\u1ed1 l\u1edbn d\u1ea1ng m\u1ea1nh<\/font><\/h3>\n

X\u00e9t n bi\u1ebfn ng\u1eabu nhi\u00ean \u0111\u1ed9c l\u1eadp c\u00f9ng ph\u00e2n ph\u1ed1i x\u00e1c su\u1ea5t, kh\u1ea3 t\u00edch (ngh\u0129a l\u00e0\u00a0E(|X|) <\u00a0\u221e),\u00a0lu\u1eadt s\u1ed1 l\u1edbn d\u1ea1ng m\u1ea1nh<\/i> ph\u00e1t bi\u1ec3u r\u1eb1ng trung b\u00ecnh t\u00edch l\u0169y Yn<\/sub> h\u1ed9i t\u1ee5 g\u1ea7n nh\u01b0 ch\u1eafc ch\u1eafn v\u1ec1 E(X).<\/p>\n

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(T\u00e0i li\u1ec7u tham kh\u1ea3o:\u00a0T\u1eeb \u0111i\u1ec3n Kinh t\u1ebf h\u1ecdc, NXB \u0110\u1ea1i h\u1ecdc Kinh t\u1ebf Qu\u1ed1c d\u00e2n; Law Of Large Numbers, Investopedia; Wikipedia)<\/i><\/p>\n<\/p><\/div>\n","protected":false},"excerpt":{"rendered":"

\n Qui lu\u1eadt s\u1ed1 l\u1edbn (ti\u1ebfng Anh: Law of large numbers) theo x\u00e1c su\u1ea5t v\u00e0 th\u1ed1ng k\u00ea cho r\u1eb1ng khi k\u00edch th\u01b0\u1edbc m\u1eabu t\u0103ng l\u00ean, gi\u00e1 tr\u1ecb trung b\u00ecnh c\u1ee7a n\u00f3 s\u1ebd g\u1ea7n v\u1edbi m\u1ee9c trung b\u00ecnh c\u1ee7a to\u00e0n b\u1ed9 t\u1ed5ng 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\/25341"}],"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=25341"}],"version-history":[{"count":0,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/posts\/25341\/revisions"}],"wp:attachment":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/media?parent=25341"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/categories?post=25341"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/tags?post=25341"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}