// Numbas version: finer_feedback_settings
{"name": "Continuous RV MGF", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Continuous RV MGF", "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<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: #f8f8f8; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; display: inline !important; float: none;\">All continuous random variables have an MGF?</span></p>", "advice": "<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: #f8f8f8; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; display: inline !important; float: none;\">The MGF does not exist for some continuous distributions, that is we cannot find an interval around $s = 0$ for which $E[e^{sX}]$ exists.&nbsp; One example is the Cauchy distribution, which does not have any finite moments.</span></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {"mark": {"script": "// Reveal answers, score and advice\nthis.display.revealAnswer();\nthis.display.showScore();\nNumbas.controls.getAdvice();", "order": "before"}}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["False", "True"], "matrix": ["1", 0], "distractors": ["", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "adam bretherton", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18177/"}]}]}], "contributors": [{"name": "adam bretherton", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18177/"}]}