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@@ -801,6 +801,42 @@ var ptx_lunr_docs = [
"title": "",
"body": " A diagnostic test is developed to detect a disease present in 1.3% of the population. For a patient who has the disease, the test will accurately give a positive result 62% of the time. When the patient does not have the disease, the test will accurately give a negative result 99.4% of the time. For a patient who receives a positive test, what is the probability they have the disease? Let be the event of receiving a positive test result and be the event of having the disease. The given information is: , and . Then, using Bayes' Theorem: "
},
{
"id": "quiz-02",
"level": "1",
"url": "quiz-02.html",
"type": "Worksheet",
"number": "",
"title": "Quiz 2",
"body": " Quiz 2 The following work should be completed individually. Use of notes or textbooks is not allowed. You may use a scientific calculator, not a graphing calculator or phone app. Show all work unless instructed otherwise. Write either True or False for each of the following statements. No justification is required. Let be integers with . Then . True. Suppose is a continuous random variable with pdf and cdf . Then . True. Suppose is a random variable taking values between 0 and 6. Then . False. Consider the joint distribution for and below. Joint Distribution 0.1 0.05 0.1 0.3 0.15 0.3 Find the marginal distributions for and . Are and independent? Since , and are not independent. Suppose a continuous random variable taking values in has cdf . Find the pdf . Find . "
},
{
"id": "quiz-02-3-1",
"level": "2",
"url": "quiz-02.html#quiz-02-3-1",
"type": "Worksheet Exercise",
"number": "1",
"title": "",
"body": " Write either True or False for each of the following statements. No justification is required. Let be integers with . Then . True. Suppose is a continuous random variable with pdf and cdf . Then . True. Suppose is a random variable taking values between 0 and 6. Then . False. "
},
{
"id": "quiz-02-3-2",
"level": "2",
"url": "quiz-02.html#quiz-02-3-2",
"type": "Worksheet Exercise",
"number": "2",
"title": "",
"body": " Consider the joint distribution for and below. Joint Distribution 0.1 0.05 0.1 0.3 0.15 0.3 Find the marginal distributions for and . Are and independent? Since , and are not independent. "
},
{
"id": "quiz-02-4-1",
"level": "2",
"url": "quiz-02.html#quiz-02-4-1",
"type": "Worksheet Exercise",
"number": "3",
"title": "",
"body": " Suppose a continuous random variable taking values in has cdf . Find the pdf . Find . "
},
{
"id": "recitation-calculus-review",
"level": "1",
@@ -851,7 +887,7 @@ var ptx_lunr_docs = [
"level": "2",
"url": "recitation-calculus-review.html#thm-FTC",
"type": "Theorem",
"number": "90",
"number": "91",
"title": "Fundamental Theorem of Calculus.",
"body": " Fundamental Theorem of Calculus If is an antiderivative of i.e., if then: "
},