{"id":37653,"date":"2024-04-15T05:23:44","date_gmt":"2024-04-15T05:23:44","guid":{"rendered":"https:\/\/academicwritersbay.com\/writings\/1-the-continuous-time-gaussian-process-x-has-zero-mean-and-autocorrelation-a-find-p-xt-1\/"},"modified":"2024-04-15T05:23:44","modified_gmt":"2024-04-15T05:23:44","slug":"1-the-continuous-time-gaussian-process-x-has-zero-mean-and-autocorrelation-a-find-p-xt-1","status":"publish","type":"post","link":"https:\/\/academicwritersbay.com\/writings\/1-the-continuous-time-gaussian-process-x-has-zero-mean-and-autocorrelation-a-find-p-xt-1\/","title":{"rendered":"1. The continuous time Gaussian process x has zero mean and autocorrelation a) Find P [x(T 1 ) >\u2026"},"content":{"rendered":"<div class=\"mailmunch-forms-before-post\" style=\"display: none !important;\"><\/div>\n<p>1. The continuous time Gaussian process x has zero mean and autocorrelation<br \/> a) Find P [x(T1) > 1] and P [x(T1) > x(2T1)], with T1 = 1\/(8f0).<br \/> b) Write the expression of the average PSD of x.<br \/> 2. Let s(t) be a Gaussian random process with zero mean and PSD<br \/> The process is filtered by a filter with frequency response<br \/> With \u00a0Compute the probability that the amplitude of the signal at the filter output, y(t), lies in the range [\u22120.6, 0.6].<br \/> \u00a0<\/p>\n<div class=\"mailmunch-forms-in-post-middle\" style=\"display: none !important;\"><\/div>\n<style>.awasam-promo{background-color:#9ed5ea;color:#fff;text-align:center;padding:10px}.button{background-color:#4caf50;border:none;color:#fff;padding:10px 20px;text-align:center;text-decoration:none;display:inline-block;font-size:16px;margin:4px 2px;cursor:pointer;border-radius:10px}.awasam-alert{color:red}<\/style>\n<div class=\"awasam-promo\">\n<h3>&#8220;Is this question part of your assignment?<strong style=\"color: red\"> We can help&#8221;<\/strong> <\/h3>\n<\/p><\/div>\n<\/p>\n<div class=\"mailmunch-forms-after-post\" style=\"display: none !important;\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>1. The continuous time Gaussian process x has zero mean and autocorrelation a) Find P [x(T1) > 1] and P [x(T1) > x(2T1)], with T1 = 1\/(8f0). b) Write the expression of the average PSD of x. 2. Let s(t) be a Gaussian random process with zero mean and PSD The process is filtered by &#8230; <a title=\"1. The continuous time Gaussian process x has zero mean and autocorrelation a) Find P [x(T 1 ) &gt;\u2026\" class=\"read-more\" href=\"https:\/\/academicwritersbay.com\/writings\/1-the-continuous-time-gaussian-process-x-has-zero-mean-and-autocorrelation-a-find-p-xt-1\/\" aria-label=\"Read more about 1. The continuous time Gaussian process x has zero mean and autocorrelation a) Find P [x(T 1 ) &gt;\u2026\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-37653","post","type-post","status-publish","format-standard","hentry","category-essaywr"],"_links":{"self":[{"href":"https:\/\/academicwritersbay.com\/writings\/wp-json\/wp\/v2\/posts\/37653","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/academicwritersbay.com\/writings\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/academicwritersbay.com\/writings\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/academicwritersbay.com\/writings\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/academicwritersbay.com\/writings\/wp-json\/wp\/v2\/comments?post=37653"}],"version-history":[{"count":0,"href":"https:\/\/academicwritersbay.com\/writings\/wp-json\/wp\/v2\/posts\/37653\/revisions"}],"wp:attachment":[{"href":"https:\/\/academicwritersbay.com\/writings\/wp-json\/wp\/v2\/media?parent=37653"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/academicwritersbay.com\/writings\/wp-json\/wp\/v2\/categories?post=37653"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/academicwritersbay.com\/writings\/wp-json\/wp\/v2\/tags?post=37653"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}