{"id":22026,"date":"2016-12-26T10:46:16","date_gmt":"2016-12-26T15:46:16","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/estg1003\/?p=1619"},"modified":"2026-04-04T10:56:17","modified_gmt":"2026-04-04T15:56:17","slug":"correlacion-multiplicacion-de-procesos","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/algoritmos101\/stp-u02eva\/correlacion-multiplicacion-de-procesos\/","title":{"rendered":"correlacion multiplicaci\u00f3n de procesos"},"content":{"rendered":"<p><em><strong>Referencia<\/strong><\/em>: Problema Le\u00f3n Garc\u00eda 10.10 p.636<\/p>\n<p>Sean X(t) y Y(t) procesos independientes estacionarios en el sentido amplio.<\/p>\n<p>Defina Z(t) = X(t) Y(t)<\/p>\n<p>a) Muestre que Z(t) es estacionario en el sentido amplio (WSS).<\/p>\n<p>b) Encuentre R<sub>Z<\/sub>(\u03c4) y S<sub>Z<\/sub>(f)<\/p>\n<p><em><strong>Soluci\u00f3n propuesta<\/strong><\/em>:<\/p>\n<p>E[Z(t)] = E[X(t) Y(t)]<\/p>\n<p>que por ser independientes,<\/p>\n<p>= E[ X(t) ] E[ Y(t) ] = m<sub>X<\/sub> m<sub>Y<\/sub><\/p>\n<p>R<sub>Z<\/sub>(\u03c4) = E[ Z(t) Z(t+\u03c4) ]<br \/>\n= E[ X(t)Y(t) X(t+\u03c4)Y(t+\u03c4) ]<br \/>\n= E[ X(t)X(t+\u03c4) Y(t)Y(t+\u03c4) ]<br \/>\n= E[ X(t)X(t+\u03c4)] E[ Y(t)Y(t+\u03c4) ]<br \/>\n= R<sub>X<\/sub>(\u03c4) R<sub>Y<\/sub>(\u03c4)<\/p>\n<p>que tambien dependen solo de \u03c4, por lo que Z(t) es WSS<\/p>\n<p>S<sub>Z<\/sub>(f) = F[R<sub>Z<\/sub>(\u03c4)]<br \/>\n= F[R<sub>X<\/sub>(\u03c4) R<sub>Y<\/sub>(\u03c4)]<br \/>\n= S<sub>X<\/sub>(f) * S<sub>Y<\/sub>(f) (convoluci\u00f3n)<\/p>\n<p><strong>Referencia<\/strong>:\u00a0Convolutions | Why X+Y in probability is a beautiful mess. 3Blue1Brown. 27-Junio-2023.<\/p>\n<p><iframe loading=\"lazy\" title=\"Convolutions | Why X+Y in probability is a beautiful mess\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/IaSGqQa5O-M?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Referencia: Problema Le\u00f3n Garc\u00eda 10.10 p.636 Sean X(t) y Y(t) procesos independientes estacionarios en el sentido amplio. Defina Z(t) = X(t) Y(t) a) Muestre que Z(t) es estacionario en el sentido amplio (WSS). b) Encuentre RZ(\u03c4) y SZ(f) Soluci\u00f3n propuesta: E[Z(t)] = E[X(t) Y(t)] que por ser independientes, = E[ X(t) ] E[ Y(t) ] [&hellip;]<\/p>\n","protected":false},"author":8043,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"wp-custom-template-entrada-stp-unidades","format":"standard","meta":{"footnotes":""},"categories":[214],"tags":[],"class_list":["post-22026","post","type-post","status-publish","format-standard","hentry","category-stp-u02eva"],"_links":{"self":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/22026","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/users\/8043"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/comments?post=22026"}],"version-history":[{"count":1,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/22026\/revisions"}],"predecessor-version":[{"id":22135,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/22026\/revisions\/22135"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/media?parent=22026"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/categories?post=22026"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/tags?post=22026"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}