// Numbas version: finer_feedback_settings
{"name": "Interactive thinned Poisson process", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Interactive thinned Poisson process", "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Assume that power surges occur as a Poisson process with average rate $\\var{a}$ per hour.</p>\n<p>The power surge causes damage to a computer system with a probability of $\\var{b}$ independently of other surges.</p>\n<p>Answer the following (P<span style=\"color: #1d1c1d; font-family: Slack-Lato, Slack-Fractions, appleLogo, sans-serif; font-size: 15px; font-style: normal; font-variant-ligatures: common-ligatures; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: #ffffff; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; display: inline !important; float: none;\">lease give exact expressions)</span>:</p>", "advice": "", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(3..6)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(1..9)/10", "description": "", "templateType": "anything", "can_override": false}, "t": {"name": "t", "group": "Ungrouped variables", "definition": "random(3..6)*10", "description": "", "templateType": "anything", "can_override": false}, "x": {"name": "x", "group": "Ungrouped variables", "definition": "random(1..3)", "description": "", "templateType": "anything", "can_override": false}, "t2": {"name": "t2", "group": "Ungrouped variables", "definition": "t/random(2,4,5)", "description": "", "templateType": "anything", "can_override": false}, "y": {"name": "y", "group": "Ungrouped variables", "definition": "random(2..a)", "description": "", "templateType": "anything", "can_override": false}, "m": {"name": "m", "group": "Ungrouped variables", "definition": "rational(1- exp(-a*(t/60)))", "description": "", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "t2/t", "description": "", "templateType": "anything", "can_override": false}, "o": {"name": "o", "group": "Ungrouped variables", "definition": "(t/60)*a*(1-b)", "description": "", "templateType": "anything", "can_override": false}, "p": {"name": "p", "group": "Ungrouped variables", "definition": "y*b + (1-(t/60))*a*b", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "t", "x", "t2", "y", "m", "n", "o", "p"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {"mark": {"script": "// Reveal answers, score and advice\nthis.display.revealAnswer();\nthis.display.showScore();\nNumbas.controls.getAdvice();", "order": "after"}}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is the probability of getting at least 1 power surge in $\\var{t}$ minutes?</p>\n<p>[[0]]</p>\n<p>If exactly 1 damaging power surge happens in $\\var{t}$ minutes, what is the probability that it occurred in the first $\\var{t2}$ minutes?</p>\n<p>[[1]]</p>\n<p>If exactly $\\var{x}$ damaging power surges happens in $\\var{t}$ minutes, what is the expected number of non-damaging power surges occurring during the same time?</p>\n<p>[[2]]</p>\n<p>if exactly $\\var{y}$ power surges happens in the first $\\var{t}$ minutes of an hour, what is the expected number of damaging power surges over the entire hour?</p>\n<p>[[3]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {"mark": {"script": "this.display.revealAnswer();", "order": "after"}}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "1-exp(-{a}*{t}/60)", "showPreview": true, "checkingType": "dp", "checkingAccuracy": 3, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {"mark": {"script": "this.display.revealAnswer();", "order": "before"}}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{t2}/{t}", "showPreview": true, "checkingType": "dp", "checkingAccuracy": 3, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {"mark": {"script": "this.display.revealAnswer();", "order": "before"}}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "({t}/60)*{a}*(1-{b})", "showPreview": true, "checkingType": "dp", "checkingAccuracy": 3, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {"mark": {"script": "this.display.revealAnswer();", "order": "before"}}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{y}*{b} + (1-({t}/60))*{a}*{b}", "showPreview": true, "checkingType": "dp", "checkingAccuracy": 3, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Chris Drovandi", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/9840/"}, {"name": "adam bretherton", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18177/"}]}]}], "contributors": [{"name": "Chris Drovandi", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/9840/"}, {"name": "adam bretherton", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18177/"}]}