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PDF Editor FAQ

What is a class size paradox w.r.t probability mass function, and how do we eliminate this?

I’ve never heard it called this. The idea is that if you randomly sample students (or even take a census of all students) and ask each respondent how many students are in their current class, the average of the responses is an overestimate of the average class size (as defined by total students / total classes).This is easy to see. Suppose there are three classes: one with 5 students, one with 10 students, and one with 15 students. The average class size is 10. But if we survey all the students about their class size, we get 5 5’s, 10 10’s, and 15 15’s. The average of these numbers is (5 x 5 + 10 x 10 + 15 x 15) / 30 = 11.67. The estimate is biased upwards because the larger classes are overweighted in the average.A similar situation arises if the estimate is based on a random sample of students — students from larger classes are disproportionately likely to enter the sample. Exercise: show that the right estimate to use with such data is the harmonic mean.

Is it possible for a teacher to take the AP exam (the one by the College Board) with students?

There is really no reason to do so. College board provides AP teachers with a variety of tools, including access to past exams with commentsTeaching AP for the First Time?Look at the resources on your course's exam page where you can see past test questions, sample student responses with commentary on the grades received, scoring guidelines and rubrics, and more.Once your course is authorized through the Course Audit process, you will have access to one or more full practice exams, a great resource for you and your students.

From a high school teacher's perspective, what would you think of a student writing about the legalization of marijuana? I want to write about this topic for a final AP assignment, and my teacher didn't tell us what not to write. Should I ask?

Let's "Start with the end in mind" (Covey)Here are exam sample responses and scoring the past two years:2017 AP English Language & Composition - Sample Student Responses & ScoringSource: https://secure-media.collegeboard.org/digitalServices/pdf/ap/ap17-english-language-q1.pdf2016 AP English Language & Composition - Sample Student Responses & ScoringSource: https://secure-media.collegeboard.org/digitalServices/pdf/ap/apcentral/ap16_english_language_q1.pdfAP EXAM: Section IIFree Response — 3 Free-Response Questions | 2 Hours, 15 Minutes (includes a 15-minute reading period) | 55% of Exam ScoreThis section has three prompts:Synthesis: Students read several texts about a topic and create an argument that synthesizes at least three of the sources to support their thesis.Rhetorical analysis: Students read a non-fiction text and analyze how the writer's language choices contribute to his or her purpose and intended meaning for the text.Argument: Students create an evidence-based argument that responds to a given topic.Source: AP English Language and Composition: The ExamNow, let's look at your 3-part question: "what would you think of a student writing about the legalization of marijuana? I want to write about this topic for a final AP assignment, and my teacher didn't tell us what not to write. Should I ask?"What do *I* think? Meh! I live in a state where marijuana is legal.If you’re interested→Law: Washington State Liquor and Cannabis BoardIf your teacher didn't tell you, then one could *assume* you could write about anything. However, if you think you're going to spring a surprise on them and shock your teacher by your subject matter, I can most assuredly say you'd be wrong. The fact that you’re asking Quora, tells me you have reservations….Your proposed topic is "safely controversial", meaning it's been done over and over and over again. You're going to have to really stretch your own thinking before you think “marijuana” is going to even get a rise in your teacher's pulse, if that were your goal.And, quite honestly, the subject doesn't matter because it is your thesis, analysis, and evidence-based argument that is being evaluated.Lasly, why wouldn't you "ask" your teacher?Most AP teachers want you to learn, practice, and demonstrate your understanding of the skills needed to write effectively so you can PASS the AP examination they're charged with preparing you for!Your working WITH your instructor will GREATLY assist in your writing, your class, your AP Exam, and future learning opportunities.Best of luck to you!

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