Calculate the probability that $$P(X\le 25,Y\le25)$$ I am unsure how to get started on this question. Any help will be greatly appreciated.
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HINT: The probability will be ratio of area of $\{(x,y):x^2+y^2\leq2000^2\}\cap((-\infty,250]\times(-\infty,250])$ to the area of $\{(x,y):x^2+y^2\leq2000^2\}$.
Przemysław Scherwentke
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Hint: The equation $$x^2 + y^2 \leq 2000^2$$ describes the area of a circle centered at the origin with radius $2000$.
Since the distribution is uniform, the probability density function is going to be $$f(x, y) = \dfrac{1}{A}$$ over all appropriate values of $x$ and $y$ (which I will leave for you to find), where $A$ is the area of the circle.
From here, all you need to do is integrate $f(x, y)$ appropriately to obtain your desired probability. However, you will need to be cautious about the bounds you choose.
Clarinetist
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and would $$P(X\le 250)$$ be calculated by $$\frac{xy}{A^{2}}$$? where y = 2000 and x = 250? – user12321 Mar 30 '18 at 13:41
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I have chosen my bounds to be 250 and -2000 on both of the integrals – user12321 Mar 30 '18 at 14:04