A (fairly good) dart thrower repeatedly throws a dart at a dart board consisting of the unit disk D= {(x,y) E R² : x² + y?

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A (fairly good) dart thrower repeatedly throws a dart at a dart<br>board consisting of the unit disk D= {(x,y) E R² : x² + y? < 1}. The<br>probability density function is<br>C(1 – x? – y?) if x² + y? < 1,<br>f(x, y) = {t<br>otherwise.<br>This means that the probability that the dart hits a region RC R? is<br>equal to SSR f(x, y) dA.<br>What is the probability that the dart misses the dartboard D?<br>What is the value of the (positive) constant C?<br>What is the probability that the dart lands within a distance of<br>! from the center of the dart board?<br>

Extracted text: A (fairly good) dart thrower repeatedly throws a dart at a dart board consisting of the unit disk D= {(x,y) E R² : x² + y? < 1}.="" the="" probability="" density="" function="" is="" c(1="" –="" x?="" –="" y?)="" if="" x²="" +="" y?="">< 1,="" f(x,="" y)="{t" otherwise.="" this="" means="" that="" the="" probability="" that="" the="" dart="" hits="" a="" region="" rc="" r?="" is="" equal="" to="" ssr="" f(x,="" y)="" da.="" what="" is="" the="" probability="" that="" the="" dart="" misses="" the="" dartboard="" d?="" what="" is="" the="" value="" of="" the="" (positive)="" constant="" c?="" what="" is="" the="" probability="" that="" the="" dart="" lands="" within="" a="" distance="" of="" !="" from="" the="" center="" of="" the="" dart="">

Jun 04, 2022

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A (fairly good) dart thrower repeatedly throws a dart at a dart board consisting of the unit disk D= {(x,y) E R² : x² + y?

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