Multivariable question -. A (fairly good) dart thrower repeatedly throws a dart at a dartboard consisting of the unit disk D= {(x, y) E R² : x² + y? < 1}. Theprobability density function isS(1 – x² – y²) if æ² + y? < 1,| 0f (r, y) =otherwise.This means that the probability that the dart hits a region RC R² isequal to fSR 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 offrom the center of the dart board?

The probability density function is fx,y=C1-x2-y2, if x2+y2≤10,…

Answered: -. A (fairly good) dart thrower…

A First Course in Probability (10th Edition)

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Author:Sheldon Ross

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Chapter1: Combinatorial Analysis

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Multivariable question

-. 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
S(1 – x² – y²) if æ² + y? < 1,
| 0
f (r, y) =
otherwise.
This means that the probability that the dart hits a region RC R² is
equal to fSR 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 board?

Expert Solution

Given data,

The probability density function is $f (x, y) = \{\begin{cases} C (1 - x^{2} - y^{2}), if (x^{2} + y^{2} \leq 1) \\ 0, otherwise \end{cases}$
The probability that a of region $R \subseteq ℝ^{2}$ is $\iint_{R} f (x, y) d A$

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