{"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. $$\\int\\limits_0^{\\text{t}} {{{\\text{f}}_1}\\left( {\\text{x}} \\right){{\\text{f}}_2}\\left( {{\\text{t}} – {\\text{x}}} \\right){\\text{dx}}} $$ D. $$\\max \\left\\{ {{{\\text{f}}_1}\\left( {\\text{t}} \\right),\\,{{\\text{f}}_2}\\left( {\\text{t}} \\right)} \\right\\}$$"},"content":{"rendered":"

[amp_mcq option1=”$${{\\text{f}}_1}\\left( {\\text{t}} \\right) + {{\\text{f}}_2}\\left( {\\text{t}} \\right)$$” option2=”$$\\int\\limits_0^{\\text{t}} {{{\\text{f}}_1}\\left( {\\text{x}} \\right){{\\text{f}}_2}\\left( {\\text{x}} \\right){\\text{dx}}} $$” option3=”$$\\int\\limits_0^{\\text{t}} {{{\\text{f}}_1}\\left( {\\text{x}} \\right){{\\text{f}}_2}\\left( {{\\text{t}} – {\\text{x}}} \\right){\\text{dx}}} $$” option4=”$$\\max \\left\\{ {{{\\text{f}}_1}\\left( {\\text{t}} \\right),\\,{{\\text{f}}_2}\\left( {\\text{t}} \\right)} \\right\\}$$” correct=”option2″]<\/p>\n

The correct answer is $\\int\\limits_0^{\\text{t}} {{{\\text{f}}_1}\\left( {\\text{x}} \\right){{\\text{f}}_2}\\left( {{\\text{t}} – {\\text{x}}} \\right){\\text{dx}}}$.<\/p>\n

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

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, $t – x$. This probability is given by the product of the probability density functions of the two modules, $f_1(x)$ and $f_2(t – x)$, integrated over the interval $[0, t]$.<\/p>\n

$$\\int\\limits_0^{\\text{t}} {{{\\text{f}}_1}\\left( {\\text{x}} \\right){{\\text{f}}_2}\\left( {{\\text{t}} – {\\text{x}}} \\right){\\text{dx}}}$$<\/p>\n

This is the probability density function of the overall time taken to execute the program.<\/p>\n","protected":false},"excerpt":{"rendered":"

[amp_mcq option1=”$${{\\text{f}}_1}\\left( {\\text{t}} \\right) + {{\\text{f}}_2}\\left( {\\text{t}} \\right)$$” option2=”$$\\int\\limits_0^{\\text{t}} {{{\\text{f}}_1}\\left( {\\text{x}} \\right){{\\text{f}}_2}\\left( {\\text{x}} \\right){\\text{dx}}} $$” option3=”$$\\int\\limits_0^{\\text{t}} {{{\\text{f}}_1}\\left( {\\text{x}} \\right){{\\text{f}}_2}\\left( {{\\text{t}} – {\\text{x}}} \\right){\\text{dx}}} $$” option4=”$$\\max \\left\\{ {{{\\text{f}}_1}\\left( {\\text{t}} \\right),\\,{{\\text{f}}_2}\\left( {\\text{t}} \\right)} \\right\\}$$” correct=”option2″]<\/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":[],"class_list":["post-20313","post","type-post","status-publish","format-standard","hentry","category-probability-and-statistics","no-featured-image-padding"],"yoast_head":"\nA 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. 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