{"id":925,"date":"2016-08-24T12:27:38","date_gmt":"2016-08-24T17:27:38","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/estg1003\/?p=925"},"modified":"2026-04-05T16:15:23","modified_gmt":"2026-04-05T21:15:23","slug":"1eva2011tii_t2-fiec-funcion-densidad","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/algoritmos101\/stp-1eva\/1eva2011tii_t2-fiec-funcion-densidad\/","title":{"rendered":"1Eva2011TII_T2 FIEC Funcion densidad"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">1ra Evaluaci\u00f3n II T\u00e9rmino 2011-2012. Diciembre 1, 2011. FIEC03236<\/h2>\n\n\n\n<p><strong>Tema 2<\/strong> (40 puntos).&nbsp; La variable aleatoria <strong>X<\/strong> tiene por funci\u00f3n densidad f<sub>X<\/sub>(x), se define la variable aleatoria <strong>Y<\/strong>=g(X)<\/p>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> f_X(x) = \\begin{cases} x+1 &amp;&amp; x \\in (-1,0] \\\\ -x+1 &amp;&amp; x \\in (0,1] \\\\ 0 &amp;&amp; x \\in (-\\infty, -1] \\cup (1,\\infty) \\end{cases} <\/span>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> g(x) = \\begin{cases} 1 &amp;&amp; x \\in (1\/2,\\infty] \\\\ 0 &amp;&amp; x \\in (-1\/2,1\/2] \\\\ -1 &amp;&amp; x \\in (-\\infty, -1\/2] \\end{cases} <\/span>\n\n\n\n<p>a) Determinar <strong>b<\/strong> para que P(|X|&lt;b) = 1\/4 (10 puntos)<\/p>\n\n\n\n<p>b) Encuentre y grafique f<sub>Y<\/sub>(y), F<sub>Y<\/sub>(y) (15 puntos)<\/p>\n\n\n\n<p>c) Si g(x)=<strong>X<\/strong><sup>2<\/sup>, encuentre y grafique la funci\u00f3n de distribuci\u00f3n y la funci\u00f3n de densidad de <strong>Y<\/strong> (15 puntos)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>1ra Evaluaci\u00f3n II T\u00e9rmino 2011-2012. Diciembre 1, 2011. FIEC03236 Tema 2 (40 puntos).&nbsp; La variable aleatoria X tiene por funci\u00f3n densidad fX(x), se define la variable aleatoria Y=g(X) a) Determinar b para que P(|X|&lt;b) = 1\/4 (10 puntos) b) Encuentre y grafique fY(y), FY(y) (15 puntos) c) Si g(x)=X2, encuentre y grafique la funci\u00f3n de [&hellip;]<\/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":[208],"tags":[],"class_list":["post-925","post","type-post","status-publish","format-standard","hentry","category-stp-1eva"],"_links":{"self":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/925","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=925"}],"version-history":[{"count":4,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/925\/revisions"}],"predecessor-version":[{"id":23487,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/925\/revisions\/23487"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/media?parent=925"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/categories?post=925"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/tags?post=925"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}