{"id":24037,"date":"2023-12-06T09:05:35","date_gmt":"2023-12-06T09:05:35","guid":{"rendered":"https:\/\/masterskills.org\/blog\/bien-ngau-nhien-random-variable-la-gi-dac-diem.html"},"modified":"2023-12-22T09:30:39","modified_gmt":"2023-12-22T02:30:39","slug":"bien-ngau-nhien-random-variable-la-gi-dac-diem","status":"publish","type":"post","link":"https:\/\/masterskills.org\/blog\/bien-ngau-nhien-random-variable-la-gi-dac-diem.html","title":{"rendered":"Bi\u1ebfn ng\u1eabu nhi\u00ean (Random Variable) l\u00e0 g\u00ec? \u0110\u1eb7c \u0111i\u1ec3m"},"content":{"rendered":"
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\u1ea2nh minh h\u1ecda. Ngu\u1ed3n: Wikipedia.<\/p>\n<\/div>\n<\/div>\n

Bi\u1ebfn ng\u1eabu nhi\u00ean<\/font><\/b><\/h2>\n

Kh\u00e1i ni\u1ec7m<\/b><\/p>\n

Bi\u1ebfn ng\u1eabu nhi\u00ean <\/b>trong ti\u1ebfng Anh l\u00e0\u00a0Random variable.<\/b><\/p>\n

Bi\u1ebfn ng\u1eabu nhi\u00ean<\/b> l\u00e0 m\u1ed9t bi\u1ebfn c\u00f3 gi\u00e1 tr\u1ecb kh\u00f4ng x\u00e1c \u0111\u1ecbnh ho\u1eb7c m\u1ed9t h\u00e0m s\u1ed1 g\u00e1n gi\u00e1 tr\u1ecb cho t\u1eebng k\u1ebft qu\u1ea3 c\u1ee7a m\u1ed9t th\u00ed nghi\u1ec7m. C\u00e1c bi\u1ebfn ng\u1eabu nhi\u00ean th\u01b0\u1eddng \u0111\u01b0\u1ee3c ch\u1ec9 \u0111\u1ecbnh b\u1eb1ng c\u00e1c ch\u1eef c\u00e1i v\u00e0 c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c ph\u00e2n lo\u1ea1i l\u00e0 bi\u1ebfn r\u1eddi r\u1ea1c (c\u00e1c bi\u1ebfn c\u00f3 gi\u00e1 tr\u1ecb c\u1ee5 th\u1ec3) ho\u1eb7c li\u00ean t\u1ee5c (c\u00e1c bi\u1ebfn c\u00f3 th\u1ec3 c\u00f3 b\u1ea5t k\u00ec gi\u00e1 tr\u1ecb n\u00e0o trong ph\u1ea1m vi li\u00ean t\u1ee5c).<\/p>\n

C\u00e1c bi\u1ebfn ng\u1eabu nhi\u00ean th\u01b0\u1eddng \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng trong ph\u00e2n t\u00edch kinh t\u1ebf l\u01b0\u1ee3ng ho\u1eb7c h\u1ed3i qui \u0111\u1ec3 x\u00e1c \u0111\u1ecbnh m\u1ed1i quan h\u1ec7 th\u1ed1ng k\u00ea v\u1edbi nhau.<\/p>\n

\u0110\u1eb7c \u0111i\u1ec3m c\u1ee7a bi\u1ebfn ng\u1eabu nhi\u00ean<\/font><\/b><\/h3>\n

Trong x\u00e1c su\u1ea5t v\u00e0 th\u1ed1ng k\u00ea, c\u00e1c bi\u1ebfn ng\u1eabu nhi\u00ean \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 \u0111\u1ecbnh l\u01b0\u1ee3ng k\u1ebft qu\u1ea3 c\u1ee7a s\u1ef1 xu\u1ea5t hi\u1ec7n ng\u1eabu nhi\u00ean v\u00e0 do \u0111\u00f3, c\u00f3 th\u1ec3 c\u00f3 nhi\u1ec1u gi\u00e1 tr\u1ecb. C\u00e1c bi\u1ebfn ng\u1eabu nhi\u00ean \u0111\u01b0\u1ee3c y\u00eau c\u1ea7u ph\u1ea3i \u0111o l\u01b0\u1eddng \u0111\u01b0\u1ee3c v\u00e0 th\u01b0\u1eddng l\u00e0 c\u00e1c s\u1ed1 th\u1ef1c.\u00a0<\/p>\n

V\u00ed d\u1ee5, ch\u1eef X c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c ch\u1ec9 \u0111\u1ecbnh \u0111\u1ec3 bi\u1ec3u th\u1ecb t\u1ea5t c\u1ea3 c\u00e1c k\u1ebft qu\u1ea3 sau khi ba con x\u00fac x\u1eafc \u0111\u01b0\u1ee3c tung ra. Trong tr\u01b0\u1eddng h\u1ee3p n\u00e0y, X c\u00f3 th\u1ec3 l\u00e0 3 (1 + 1+ 1), 18 (6 + 6 + 6) ho\u1eb7c m\u1ed9t con s\u1ed1 b\u1ea5t k\u00ec gi\u1eefa 3 v\u00e0 18, v\u00ec s\u1ed1 l\u1edbn nh\u1ea5t tr\u00ean x\u00fac x\u1eafc l\u00e0 l\u00e0 6 v\u00e0 s\u1ed1 b\u00e9 nh\u1ea5t l\u00e0 1.<\/p>\n

Bi\u1ebfn ng\u1eabu nhi\u00ean kh\u00e1c v\u1edbi bi\u1ebfn \u0111\u1ea1i s\u1ed1. Bi\u1ebfn trong m\u1ed9t ph\u01b0\u01a1ng tr\u00ecnh \u0111\u1ea1i s\u1ed1 l\u00e0 m\u1ed9t gi\u00e1 tr\u1ecb kh\u00f4ng x\u00e1c \u0111\u1ecbnh c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c t\u00ednh to\u00e1n. Ph\u01b0\u01a1ng tr\u00ecnh 10 + x = 13 cho th\u1ea5y ch\u00fang ta c\u00f3 th\u1ec3 t\u00ednh gi\u00e1 tr\u1ecb c\u1ee5 th\u1ec3 cho x l\u00e0 3. M\u1eb7t kh\u00e1c, m\u1ed9t bi\u1ebfn ng\u1eabu nhi\u00ean c\u00f3 nhi\u1ec1u gi\u00e1 tr\u1ecb v\u00e0 b\u1ea5t k\u00ec gi\u00e1 tr\u1ecb n\u00e0o trong s\u1ed1 \u0111\u00f3 c\u0169ng c\u00f3 th\u1ec3 l\u00e0 k\u1ebft qu\u1ea3 nh\u01b0 trong v\u00ed d\u1ee5 x\u00fac x\u1eafc \u1edf tr\u00ean.<\/p>\n

Trong th\u1ebf gi\u1edbi doanh nghi\u1ec7p, c\u00e1c bi\u1ebfn ng\u1eabu nhi\u00ean c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c g\u00e1n cho c\u00e1c thu\u1ed9c t\u00ednh nh\u01b0 gi\u00e1 trung b\u00ecnh c\u1ee7a t\u00e0i s\u1ea3n trong m\u1ed9t kho\u1ea3ng th\u1eddi gian nh\u1ea5t \u0111\u1ecbnh, l\u1ee3i t\u1ee9c \u0111\u1ea7u t\u01b0 sau m\u1ed9t s\u1ed1 n\u0103m nh\u1ea5t \u0111\u1ecbnh, t\u1ec9 l\u1ec7 doanh thu \u01b0\u1edbc t\u00ednh t\u1ea1i m\u1ed9t c\u00f4ng ty trong 6 th\u00e1ng sau, vv.\u00a0<\/p>\n

C\u00e1c nh\u00e0 ph\u00e2n t\u00edch r\u1ee7i ro ch\u1ec9 \u0111\u1ecbnh c\u00e1c bi\u1ebfn ng\u1eabu nhi\u00ean cho c\u00e1c m\u00f4 h\u00ecnh r\u1ee7i ro khi h\u1ecd mu\u1ed1n \u01b0\u1edbc t\u00ednh kh\u1ea3 n\u0103ng x\u1ea3y ra s\u1ef1 ki\u1ec7n b\u1ea5t l\u1ee3i. C\u00e1c bi\u1ebfn n\u00e0y \u0111\u01b0\u1ee3c tr\u00ecnh b\u00e0y b\u1eb1ng c\u00e1c c\u00f4ng c\u1ee5 nh\u01b0 b\u1ea3ng ph\u00e2n t\u00edch \u0111\u1ed9 nh\u1ea1y v\u00e0 k\u1ecbch b\u1ea3n m\u00e0 c\u00e1c nh\u00e0 qu\u1ea3n l\u00ed r\u1ee7i ro s\u1eed d\u1ee5ng \u0111\u1ec3 \u0111\u01b0a ra c\u00e1c quy\u1ebft \u0111\u1ecbnh li\u00ean quan \u0111\u1ebfn gi\u1ea3m thi\u1ec3u r\u1ee7i ro.<\/p>\n

V\u00ed d\u1ee5 v\u1ec1 bi\u1ebfn ng\u1eabu nhi\u00ean<\/font><\/b><\/h3>\n

M\u1ed9t v\u00ed d\u1ee5 \u0111i\u1ec3n h\u00ecnh c\u1ee7a bi\u1ebfn ng\u1eabu nhi\u00ean l\u00e0 k\u1ebft qu\u1ea3 c\u1ee7a vi\u1ec7c tung \u0111\u1ed3ng xu. L\u1ea5y v\u00ed d\u1ee5 ph\u00e2n ph\u1ed1i x\u00e1c su\u1ea5t trong \u0111\u00f3 k\u1ebft qu\u1ea3 c\u1ee7a m\u1ed9t s\u1ef1 ki\u1ec7n ng\u1eabu nhi\u00ean kh\u00f4ng c\u00f3 kh\u1ea3 n\u0103ng x\u1ea3y ra l\u00e0 nh\u01b0 nhau. N\u1ebfu bi\u1ebfn ng\u1eabu nhi\u00ean, Y, l\u00e0 s\u1ed1 l\u01b0\u1ee3ng m\u1eb7t tr\u01b0\u1edbc ch\u00fang ta nh\u1eadn \u0111\u01b0\u1ee3c t\u1eeb vi\u1ec7c n\u00e9m hai \u0111\u1ed3ng xu, th\u00ec Y c\u00f3 th\u1ec3 l\u00e0 0, 1 ho\u1eb7c 2. \u0110i\u1ec1u n\u00e0y c\u00f3 ngh\u0129a l\u00e0 ch\u00fang ta c\u00f3 th\u1ec3 kh\u00f4ng c\u00f3 m\u1eb7t tr\u01b0\u1edbc, m\u1ed9t m\u1eb7t tr\u01b0\u1edbc ho\u1eb7c c\u1ea3 hai m\u1eb7t tr\u01b0\u1edbc trong c\u00f9ng m\u1ed9t l\u1ea7n n\u00e9m hai \u0111\u1ed3ng xu.<\/p>\n

Tuy nhi\u00ean, hai \u0111\u1ed3ng xu r\u01a1i xu\u1ed1ng theo b\u1ed1n c\u00e1ch kh\u00e1c nhau: SS, TT, ST, TT. Do \u0111\u00f3, P (Y = 0) = 1\/4 v\u00ec ch\u00fang ta c\u00f3 m\u1ed9t c\u01a1 h\u1ed9i kh\u00f4ng c\u00f3 m\u1eb7t tr\u01b0\u1edbc (t\u1ee9c l\u00e0, hai m\u1eb7t sau [SS] khi tung \u0111\u1ed3ng xu). T\u01b0\u01a1ng t\u1ef1, x\u00e1c su\u1ea5t l\u1ea5y \u0111\u01b0\u1ee3c hai m\u1eb7t tr\u01b0\u1edbc (TT) c\u0169ng l\u00e0 1\/4. L\u01b0u \u00fd r\u1eb1ng vi\u1ec7c l\u1ea5y \u0111\u01b0\u1ee3c m\u1ed9t m\u1eb7t tr\u01b0\u1edbc c\u00f3 kh\u1ea3 n\u0103ng x\u1ea3y ra hai l\u1ea7n: trong TS v\u00e0 ST. Trong tr\u01b0\u1eddng h\u1ee3p n\u00e0y, P (Y = 1) = 2\/4 = 1\/2.<\/p>\n

(Trong v\u00ed d\u1ee5 tr\u00ean, T l\u00e0 m\u1eb7t tr\u01b0\u1edbc, S l\u00e0 m\u1eb7t sau)<\/p>\n

(Theo\u00a0Investopedia<\/i>)<\/p>\n<\/p><\/div>\n","protected":false},"excerpt":{"rendered":"

\n Bi\u1ebfn ng\u1eabu nhi\u00ean (ti\u1ebfng Anh: Random variable) l\u00e0 m\u1ed9t bi\u1ebfn c\u00f3 gi\u00e1 tr\u1ecb kh\u00f4ng x\u00e1c \u0111\u1ecbnh ho\u1eb7c m\u1ed9t h\u00e0m s\u1ed1 g\u00e1n gi\u00e1 tr\u1ecb cho t\u1eebng k\u1ebft qu\u1ea3 c\u1ee7a m\u1ed9t th\u00ed nghi\u1ec7m.\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\/24037"}],"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=24037"}],"version-history":[{"count":0,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/posts\/24037\/revisions"}],"wp:attachment":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/media?parent=24037"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/categories?post=24037"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/tags?post=24037"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}