{"id":938,"date":"2016-09-24T12:56:21","date_gmt":"2016-09-24T17:56:21","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/estg1003\/?p=938"},"modified":"2026-04-05T16:27:57","modified_gmt":"2026-04-05T21:27:57","slug":"2eva2011tii_t1-fiec-covarianza","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/algoritmos101\/stp-2eva\/2eva2011tii_t1-fiec-covarianza\/","title":{"rendered":"2Eva2011TII_T1 FIEC covarianza"},"content":{"rendered":"\n

2da Evaluaci\u00f3n II T\u00e9rmino 2011-2012. Febrero 2, 2012. FIEC03236<\/h2>\n\n\n\n

Tema 1<\/strong> (40 puntos). Sea X<\/strong>(t) un proceso normal y estacionario de media E[X<\/strong>(t)]=0 y autocorrelaci\u00f3n<\/p>\n\n\n R_x (\\tau)= \\frac{4}{4+\\tau^2} <\/span>\n\n\n\n

a) Calcular la matriz de covarianzas de la variable aleatoria bidimensional<\/p>\n\n\n [X(-2),X(1)+5X(2)] <\/span>\n\n\n\n

b) Calcular la funci\u00f3n de densidad de la variable aleatoria: A<\/strong>=X<\/strong>(1)+5X<\/strong>(2)<\/p>\n\n\n\n

c) Sea B<\/strong> una variable aleatoria tal que P(B<\/strong>=0)=P(B<\/strong>=1)=1\/2.
Se supone que las variables aleatorias A<\/strong> y B<\/strong> son independientes.
Calcular la funci\u00f3n de densidad de la variable aleatoria C<\/strong>=A<\/strong>+B<\/strong>.<\/p>\n\n\n\n

Consideremos el sistema lineal e invariante con el tiempo cuya funci\u00f3n de transferencia es:<\/p>\n\n\n H(\\omega)=\\begin{cases} 3 && |\\omega| \\leq 1 \\\\ 0 && |\\omega|>1 \\end{cases} <\/span>\n\n\n\n

Sea Y<\/strong>(t) la salida de este sistema cuando la entrada es X<\/strong>(t).<\/p>\n\n\n\n

d) Determinar la funci\u00f3n de densidad de Y<\/strong>(t).<\/p>\n","protected":false},"excerpt":{"rendered":"

2da Evaluaci\u00f3n II T\u00e9rmino 2011-2012. Febrero 2, 2012. FIEC03236 Tema 1 (40 puntos). Sea X(t) un proceso normal y estacionario de media E[X(t)]=0 y autocorrelaci\u00f3n a) Calcular la matriz de covarianzas de la variable aleatoria bidimensional b) Calcular la funci\u00f3n de densidad de la variable aleatoria: A=X(1)+5X(2) c) Sea B una variable aleatoria tal que […]<\/p>\n","protected":false},"author":8043,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"wp-custom-template-entrada-stp-ejercicios","format":"standard","meta":{"footnotes":""},"categories":[210],"tags":[],"class_list":["post-938","post","type-post","status-publish","format-standard","hentry","category-stp-2eva"],"_links":{"self":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/938","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=938"}],"version-history":[{"count":4,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/938\/revisions"}],"predecessor-version":[{"id":23511,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/938\/revisions\/23511"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/media?parent=938"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/categories?post=938"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/tags?post=938"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}