{"id":24536,"date":"2023-12-06T12:20:06","date_gmt":"2023-12-06T12:20:06","guid":{"rendered":"https:\/\/masterskills.org\/blog\/phan-phoi-dong-nhat-uniform-distribution-la-gi-dac-diem.html"},"modified":"2023-12-22T09:50:07","modified_gmt":"2023-12-22T02:50:07","slug":"phan-phoi-dong-nhat-uniform-distribution-la-gi-dac-diem","status":"publish","type":"post","link":"https:\/\/masterskills.org\/blog\/phan-phoi-dong-nhat-uniform-distribution-la-gi-dac-diem.html","title":{"rendered":"Ph\u00e2n ph\u1ed1i \u0111\u1ed3ng nh\u1ea5t (Uniform Distribution) l\u00e0 g\u00ec? \u0110\u1eb7c \u0111i\u1ec3m"},"content":{"rendered":"
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Hi\u0300nh minh ho\u0323a. Ngu\u00f4\u0300n: Stackoverflow.com<\/p>\n<\/figcaption><\/figure>\n

Ph\u00e2n ph\u1ed1i \u0111\u1ed3ng nh\u1ea5t<\/font><\/h2>\n

Kha\u0301i ni\u1ec7m<\/b><\/p>\n

Ph\u00e2n ph\u1ed1i \u0111\u1ed3ng nh\u1ea5t <\/b>trong ti\u00ea\u0301ng Anh la\u0300 Uniform Distribution.<\/b><\/p>\n

Trong th\u1ed1ng k\u00ea, ph\u00e2n ph\u1ed1i \u0111\u1ed3ng nh\u1ea5t<\/b> l\u00e0 m\u1ed9t d\u1ea1ng ph\u00e2n ph\u1ed1i x\u00e1c su\u1ea5t th\u1ed1ng k\u00ea trong \u0111\u00f3 t\u1ea5t c\u1ea3 c\u00e1c k\u1ebft qu\u1ea3 \u0111\u1ec1u c\u00f3 kh\u1ea3 n\u0103ng x\u1ea3y ra nh\u01b0 nhau, m\u1ed7i bi\u1ebfn c\u00f3 c\u00f9ng m\u1ed9t x\u00e1c su\u1ea5t \u0111\u1ec3 cho ra m\u1ed9t k\u1ebft qu\u1ea3.\u00a0<\/p>\n

V\u00ed d\u1ee5 m\u1ed9t b\u1ed9 b\u00e0i c\u00f3 ph\u00e2n ph\u1ed1i \u0111\u1ed3ng nh\u1ea5t b\u1edfi v\u00ec kh\u1ea3 n\u0103ng r\u00fat ra m\u1ed9t l\u00e1 c\u01a1, l\u00e1 r\u00f4, l\u00e1 nh\u00e9p (chu\u1ed3n) hay l\u00e1 b\u00edch \u0111\u1ec1u nh\u01b0 nhau.\u00a0<\/p>\n

Vi\u1ec7c tung \u0111\u1ed3ng xu c\u0169ng c\u00f3 ph\u00e2n ph\u1ed1i \u0111\u1ed3ng nh\u1ea5t v\u00ec x\u00e1c su\u1ea5t xu\u1ea5t hi\u1ec7n m\u1eb7t ng\u1eeda ho\u1eb7c m\u1eb7t s\u1ea5p trong m\u1ed9t l\u1ea7n tung \u0111\u1ed3ng xu l\u00e0 nh\u01b0 nhau, v\u1edbi \u0111i\u1ec1u ki\u1ec7n \u0111\u1ed3ng xu \u0111\u00f3 l\u00e0 \u0111\u1ed3ng ch\u1ea5t. \u00a0\u00a0 <\/p>\n

Ph\u00e2n ph\u1ed1i \u0111\u1ed3ng nh\u1ea5t c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c h\u00ecnh dung tr\u1ef1c quan l\u00e0 m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng n\u1eb1m ngang, do \u0111\u00f3, khi tung \u0111\u1ed3ng xu k\u1ebft qu\u1ea3 tung \u0111\u1ed3ng xu \u0111\u01b0\u1ee3c m\u1eb7t ng\u1eeda hay m\u1eb7t x\u1ea5p \u0111\u1ec1u c\u00f3 x\u00e1c su\u1ea5t p = 0,5 v\u00e0 \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n b\u1eb1ng m\u1ed9t \u0111\u01b0\u1eddng n\u1eb1m ngang t\u1eeb m\u1ee9c 0,5 \u1edf tr\u1ee5c y.\u00a0 \u00a0\u00a0<\/i><\/p>\n

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Hi\u0300nh minh ho\u0323a. Ngu\u1ed3n: Thoughtco.com<\/p>\n<\/figcaption><\/figure>\n

Hay nh\u01b0 h\u00ecnh \u1edf tr\u00ean, k\u1ebft qu\u1ea3 xu\u1ea5t hi\u1ec7n c\u00e1c m\u1eb7t\u00a0<\/i>khi xoay m\u1ed9t con x\u00fac x\u1eafc \u0111\u1ec1u l\u00e0 1\/6.<\/i><\/p>\n

\u0110\u1eb7c \u0111i\u1ec3m Ph\u00e2n ph\u1ed1i \u0111\u1ed3ng nh\u1ea5t\u00a0<\/font><\/h3>\n

C\u00f3 hai lo\u1ea1i ph\u00e2n ph\u1ed1i \u0111\u1ed3ng nh\u1ea5t<\/b> l\u00e0 ph\u00e2n ph\u1ed1i r\u1eddi r\u1ea1c v\u00e0 ph\u00e2n ph\u1ed1i li\u00ean t\u1ee5c.\u00a0<\/p>\n

C\u00e1c k\u1ebft qu\u1ea3 c\u00f3 th\u1ec3 c\u00f3 khi xoay m\u1ed9t con x\u00fac x\u1eafc l\u00e0 m\u1ed9t v\u00ed d\u1ee5 \u0111i\u1ec3n h\u00ecnh v\u1ec1 ph\u00e2n ph\u1ed1i \u0111\u1ed3ng nh\u1ea5t r\u1eddi r\u1ea1c<\/i>.\u00a0<\/p>\n

C\u00e1c k\u1ebft qu\u1ea3 n\u00e0y ch\u1ec9 c\u00f3 th\u1ec3 l\u00e0 1, 2, 3, 4, 5 ho\u1eb7c 6 nh\u01b0ng kh\u00f4ng th\u1ec3 cho ra 2.3, 4.7 ho\u1eb7c 5.5 hay c\u00e1c k\u1ebft qu\u1ea3 c\u00f3 th\u1ec3 t\u1ea1o ra l\u00e0 h\u1eefu h\u1ea1n. Do \u0111\u00f3, con x\u00fac x\u1eafc c\u00f3 ph\u00e2n ph\u1ed1i r\u1eddi r\u1ea1c v\u1edbi p = 1\/6 cho m\u1ed7i k\u1ebft qu\u1ea3. \u00a0\u00a0<\/p>\n

Ngo\u00e0i ra, m\u1ed9t m\u00e1y ch\u1ecdn s\u1ed1 ng\u1eabu nhi\u00ean \u0111\u01b0\u1ee3c xem l\u00e0 c\u00f3 ph\u00e2n ph\u1ed1i \u0111\u1ed3ng nh\u1ea5t li\u00ean t\u1ee5c<\/i>. V\u1edbi ki\u1ec3u ph\u00e2n ph\u1ed1i n\u00e0y, m\u1ecdi bi\u1ebfn \u0111\u1ec1u c\u00f3 c\u01a1 h\u1ed9i xu\u1ea5t hi\u1ec7n nh\u01b0 nhau, nh\u01b0ng v\u1eabn c\u00f3 m\u1ed9t s\u1ed1 \u0111i\u1ec3m li\u00ean t\u1ee5c (ho\u1eb7c c\u00f3 th\u1ec3 l\u00e0 v\u00f4 h\u1ea1n) c\u00f3 th\u1ec3 t\u1ed3n t\u1ea1i.\u00a0<\/p>\n

M\u1ed9t s\u1ed1 ph\u00e2n ph\u1ed1i li\u00ean t\u1ee5c quan tr\u1ecdng nh\u01b0 ph\u00e2n ph\u1ed1i chu\u1ea9n, ph\u00e2n ph\u1ed1i chi b\u00ecnh ph\u01b0\u01a1ng v\u00e0 ph\u00e2n ph\u1ed1i T-Student.\u00a0<\/i><\/p>\n

Ph\u00e2n ph\u1ed1i \u0111\u1ed3ng nh\u1ea5t<\/b> ch\u1ec9 c\u00f3 hai k\u1ebft qu\u1ea3 c\u00f3 th\u1ec3 x\u1ea3y ra l\u00e0 m\u1ed9t tr\u01b0\u1eddng h\u1ee3p \u0111\u1eb7c bi\u1ec7t c\u1ee7a ph\u00e2n ph\u1ed1i nh\u1ecb th\u1ee9c. \u00a0<\/p>\n

C\u00f3 nhi\u1ec1u h\u00e0m x\u1eed l\u00ed d\u1eef li\u1ec7u hay ph\u00e2n t\u00edch d\u1eef li\u1ec7u li\u00ean quan \u0111\u1ebfn c\u00e1c d\u1ea1ng ph\u00e2n ph\u1ed1i \u0111\u1ec3 hi\u1ec3u r\u00f5 h\u01a1n t\u00ednh ch\u1ea5t v\u00e0 ph\u01b0\u01a1ng sai c\u00e1c bi\u1ebfn trong m\u1ed9t t\u1eadp d\u1eef li\u1ec7u.<\/p>\n

C\u00e1c h\u00e0m n\u00e0y g\u1ed3m c\u00f3 h\u00e0m m\u1eadt \u0111\u1ed9 x\u00e1c su\u1ea5t (Probability Density Function), h\u00e0m ph\u00e2n ph\u1ed1i t\u00edch l\u0169y (Cumulative Density Function)v\u00e0 h\u00e0m sinh m\u00f4 men (Moment Generating Function).\u00a0<\/i><\/p>\n

Tr\u1ef1c quan h\u00f3a Ph\u00e2n ph\u1ed1i \u0111\u1ed3ng nh\u1ea5t<\/font><\/h3>\n

Ph\u00e2n ph\u1ed1i x\u00e1c su\u1ea5t<\/b> l\u00e0 m\u1ed9t c\u00e1ch tr\u1ef1c quan h\u00f3a m\u1ed9t t\u1eadp h\u1ee3p d\u1eef li\u1ec7u d\u01b0\u1edbi d\u1ea1ng bi\u1ec3u \u0111\u1ed3 hay d\u1ea1ng danh s\u00e1ch cho bi\u1ebft kh\u1ea3 n\u0103ng x\u1ea3y ra c\u00e1c bi\u1ebfn ng\u1eabu nhi\u00ean.<\/p>\n

C\u00f3 nhi\u1ec1u lo\u1ea1i ph\u00e2n ph\u1ed1i x\u00e1c su\u1ea5t kh\u00e1c nhau, trong \u0111\u00f3 ph\u00e2n ph\u1ed1i \u0111\u1ed3ng nh\u1ea5t l\u00e0 d\u1ea1ng \u0111\u01a1n gi\u1ea3n nh\u1ea5t.\u00a0<\/i><\/p>\n

Trong m\u1ed9t ph\u00e2n ph\u1ed1i \u0111\u1ed3ng nh\u1ea5t, t\u1eadp h\u1ee3p c\u00e1c bi\u1ebfn \u0111\u1ec1u c\u00f3 kh\u1ea3 n\u0103ng x\u1ea3y ra ch\u00ednh x\u00e1c nh\u01b0 nhau. Ph\u00e2n ph\u1ed1i \u0111\u1ed3ng nh\u1ea5t khi \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n tr\u00ean bi\u1ec3u \u0111\u1ed3 d\u01b0\u1edbi d\u1ea1ng bi\u1ec3u \u0111\u1ed3 c\u1ed9t ho\u1eb7c bi\u1ec3u \u0111\u1ed3 \u0111\u01b0\u1eddng, \u1edf \u0111\u00f3 m\u1ed7i k\u1ebft qu\u1ea3 ti\u1ec1m n\u0103ng \u0111\u1ec1u c\u00f3 c\u00f9ng gi\u00e1 tr\u1ecb.<\/p>\n

Do v\u1eady, h\u00ecnh d\u1ea1ng ph\u00e2n ph\u1ed1i \u0111\u1ed3ng nh\u1ea5t tr\u00f4ng gi\u1ed1ng nh\u01b0 m\u1ed9t h\u00ecnh ch\u1eef nh\u1eadt v\u00e0 \u0111\u00f4i khi c\u00f2n \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 ph\u00e2n ph\u1ed1i h\u00ecnh ch\u1eef nh\u1eadt.\u00a0<\/p>\n

V\u00ed d\u1ee5 kh\u1ea3 n\u0103ng r\u00fat m\u1ed9t l\u00e1 c\u01a1 t\u1eeb m\u1ed9t b\u1ed9 b\u00e0i l\u00e0 ho\u00e0n to\u00e0n ng\u1eabu nhi\u00ean nh\u01b0ng x\u00e1c su\u1ea5t c\u1ee7a n\u00f3 s\u1ebd v\u1eabn b\u1eb1ng x\u00e1c su\u1ea5t r\u00fat \u0111\u01b0\u1ee3c l\u00e1 r\u00f4, l\u00e1 chu\u1ed3n v\u00e0 l\u00e1 b\u00edch – t\u1ee9c l\u00e0 1\/4.\u00a0 \u00a0<\/p>\n

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

\n Ph\u00e2n ph\u1ed1i \u0111\u1ed3ng nh\u1ea5t (ti\u1ebfng Anh: Uniform Distribution) l\u00e0 m\u1ed9t d\u1ea1ng ph\u00e2n ph\u1ed1i x\u00e1c su\u1ea5t th\u1ed1ng k\u00ea trong \u0111\u00f3 t\u1ea5t c\u1ea3 c\u00e1c k\u1ebft qu\u1ea3 \u0111\u1ec1u c\u00f3 kh\u1ea3 n\u0103ng x\u1ea3y ra nh\u01b0 nhau, m\u1ed7i bi\u1ebfn c\u00f3 c\u00f9ng m\u1ed9t x\u00e1c su\u1ea5t \u0111\u1ec3 cho ra m\u1ed9t k\u1ebft qu\u1ea3.\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\/24536"}],"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=24536"}],"version-history":[{"count":0,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/posts\/24536\/revisions"}],"wp:attachment":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/media?parent=24536"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/categories?post=24536"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/tags?post=24536"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}