{"id":20313,"date":"2024-04-15T05:51:13","date_gmt":"2024-04-15T05:51:13","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=20313"},"modified":"2024-04-15T05:51:13","modified_gmt":"2024-04-15T05:51:13","slug":"a-program-consists-of-two-modules-executed-sequentially-let-f1t-and-f2t-respectively-denote-the-probability-density-functions-of-time-taken-to-execute-the-two-modules-the-probability-density-fun","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-program-consists-of-two-modules-executed-sequentially-let-f1t-and-f2t-respectively-denote-the-probability-density-functions-of-time-taken-to-execute-the-two-modules-the-probability-density-fun\/","title":{"rendered":"A program consists of two modules executed sequentially. Let f1(t) and f2(t) respectively denote the probability density functions of time taken to execute the two modules. The probability density function of the overall time taken to execute the program is given by A. $${{\\text{f}}_1}\\left( {\\text{t}} \\right) + {{\\text{f}}_2}\\left( {\\text{t}} \\right)$$ B. $$\\int\\limits_0^{\\text{t}} {{{\\text{f}}_1}\\left( {\\text{x}} \\right){{\\text{f}}_2}\\left( {\\text{x}} \\right){\\text{dx}}} $$ C. $$\\int\\limits_0^{\\text{t}} {{{\\text{f}}_1}\\left( {\\text{x}} \\right){{\\text{f}}_2}\\left( {{\\text{t}} &#8211; {\\text{x}}} \\right){\\text{dx}}} $$ D. $$\\max \\left\\{ {{{\\text{f}}_1}\\left( {\\text{t}} \\right),\\,{{\\text{f}}_2}\\left( {\\text{t}} \\right)} \\right\\}$$"},"content":{"rendered":"<p>\r\n    <!-- Check if it's an AMP page -->\r\n            <!-- Non-AMP version -->\r\n        <div class=\"mcq-container\" data-quiz-id=\"quizState_6a999062d356f\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"false\">\r\n                    $${{\text{f}}_1}left( {\text{t}} \right) + {{\text{f}}_2}left( {\text{t}} \right)$$                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option2\" data-is-correct=\"true\">\r\n                    $$intlimits_0^{\text{t}} {{{\text{f}}_1}left( {\text{x}} \right){{\text{f}}_2}left( {\text{x}} \right){\text{dx}}} $$                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option3\" data-is-correct=\"false\">\r\n                    $$intlimits_0^{\text{t}} {{{\text{f}}_1}left( {\text{x}} \right){{\text{f}}_2}left( {{\text{t}} - {\text{x}}} \right){\text{dx}}} $$                <\/div>\r\n                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            \r\n            <!-- Feedback messages for non-AMP -->\r\n            <div class=\"feedback\" data-feedback=\"wrong\">Answer is Right!<\/div>\r\n            <div class=\"feedback\" data-feedback=\"right\">Answer is Wrong!<\/div>\r\n        <\/div>\r\n\r\n        <script>\r\n        document.addEventListener('DOMContentLoaded', function () {\r\n            var containers = document.querySelectorAll('.mcq-container');\r\n\r\n            containers.forEach(function(container) {\r\n                var options = container.querySelectorAll('.option');\r\n                var feedbackSelect = container.querySelector('[data-feedback=\"select\"]');\r\n                var feedbackWrong = container.querySelector('[data-feedback=\"wrong\"]');\r\n                var feedbackRight = container.querySelector('[data-feedback=\"right\"]');\r\n\r\n                options.forEach(function(option) {\r\n                    option.addEventListener('click', function() {\r\n                        var selectedOption = option.getAttribute('data-option-key');\r\n                        var isCorrect = option.getAttribute('data-is-correct') === 'true';\r\n\r\n                        \/\/ Remove previous selections\r\n                        options.forEach(function(opt) {\r\n                            opt.classList.remove('correct', 'incorrect');\r\n                        });\r\n\r\n                        \/\/ Add the correct\/incorrect class\r\n                        if (isCorrect) {\r\n                            option.classList.add('correct');\r\n                            feedbackRight.hidden = false;\r\n                            feedbackWrong.hidden = true;\r\n                        } else {\r\n                            option.classList.add('incorrect');\r\n                            feedbackRight.hidden = true;\r\n                            feedbackWrong.hidden = false;\r\n                        }\r\n\r\n                        \/\/ Hide select feedback\r\n                        feedbackSelect.hidden = true;\r\n                    });\r\n                });\r\n            });\r\n        });\r\n        <\/script>\r\n    \r\n    <!--more--><\/p>\n<p>The correct answer is $\\int\\limits_0^{\\text{t}} {{{\\text{f}}_1}\\left( {\\text{x}} \\right){{\\text{f}}_2}\\left( {{\\text{t}} &#8211; {\\text{x}}} \\right){\\text{dx}}}$.<\/p>\n<p>The probability density function of the overall time taken to execute the program is the probability that the program will take a certain amount of time, given that the two modules are executed sequentially. This probability can be calculated by multiplying the probability density functions of the two modules, $f_1(t)$ and $f_2(t)$, and integrating the product over the interval $[0, t]$. This is because the probability that the program will take a certain amount of time is equal to the probability that the first module takes a certain amount of time, and then the second module takes the remaining amount of time.<\/p>\n<p>The probability density function of the first module is $f_1(t)$, which gives the probability that the first module will take a certain amount of time, $t$. The probability density function of the second module is $f_2(t)$, which gives the probability that the second module will take a certain amount of time, $t$. The probability that the program will take a certain amount of time, $t$, is equal to the probability that the first module takes a certain amount of time, $x$, and then the second module takes the remaining amount of time, $t &#8211; x$. This probability is given by the product of the probability density functions of the two modules, $f_1(x)$ and $f_2(t &#8211; x)$, integrated over the interval $[0, t]$.<\/p>\n<p>$$\\int\\limits_0^{\\text{t}} {{{\\text{f}}_1}\\left( {\\text{x}} \\right){{\\text{f}}_2}\\left( {{\\text{t}} &#8211; {\\text{x}}} \\right){\\text{dx}}}$$<\/p>\n<p>This is the probability density function of the overall time taken to execute the program.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Subscribe on YouTube<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[691],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.2 (Yoast SEO v23.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>A program consists of two modules executed sequentially. Let f1(t) and f2(t) respectively denote the probability density functions of time taken to execute the two modules. The probability density function of the overall time taken to execute the program is given by A. $${{\\text{f}}_1}\\left( {\\text{t}} \\right) + {{\\text{f}}_2}\\left( {\\text{t}} \\right)$$ B. $$\\int\\limits_0^{\\text{t}} {{{\\text{f}}_1}\\left( {\\text{x}} \\right){{\\text{f}}_2}\\left( {\\text{x}} \\right){\\text{dx}}} $$ C. $$\\int\\limits_0^{\\text{t}} {{{\\text{f}}_1}\\left( {\\text{x}} \\right){{\\text{f}}_2}\\left( {{\\text{t}} - {\\text{x}}} \\right){\\text{dx}}} $$ D. $$\\max \\left\\{ {{{\\text{f}}_1}\\left( {\\text{t}} \\right),\\,{{\\text{f}}_2}\\left( {\\text{t}} \\right)} \\right\\}$$<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/a-program-consists-of-two-modules-executed-sequentially-let-f1t-and-f2t-respectively-denote-the-probability-density-functions-of-time-taken-to-execute-the-two-modules-the-probability-density-fun\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A program consists of two modules executed sequentially. Let f1(t) and f2(t) respectively denote the probability density functions of time taken to execute the two modules. The probability density function of the overall time taken to execute the program is given by A. $${{\\text{f}}_1}\\left( {\\text{t}} \\right) + {{\\text{f}}_2}\\left( {\\text{t}} \\right)$$ B. $$\\int\\limits_0^{\\text{t}} {{{\\text{f}}_1}\\left( {\\text{x}} \\right){{\\text{f}}_2}\\left( {\\text{x}} \\right){\\text{dx}}} $$ C. $$\\int\\limits_0^{\\text{t}} {{{\\text{f}}_1}\\left( {\\text{x}} \\right){{\\text{f}}_2}\\left( {{\\text{t}} - {\\text{x}}} \\right){\\text{dx}}} $$ D. $$\\max \\left\\{ {{{\\text{f}}_1}\\left( {\\text{t}} \\right),\\,{{\\text{f}}_2}\\left( {\\text{t}} \\right)} \\right\\}$$\" \/>\n<meta property=\"og:description\" content=\"Join Our Telegram Channel Subscribe on YouTube\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/a-program-consists-of-two-modules-executed-sequentially-let-f1t-and-f2t-respectively-denote-the-probability-density-functions-of-time-taken-to-execute-the-two-modules-the-probability-density-fun\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2024-04-15T05:51:13+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"A program consists of two modules executed sequentially. 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Let f1(t) and f2(t) respectively denote the probability density functions of time taken to execute the two modules. 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