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Consider two independent random variables $X$ and $Y$ having probability density functions uniform in the interval $[-1, 1]$. The probability that $X^{2}+Y^{2}>1$ is 

  1. $\pi/4$
  2. $1-\pi/4$
  3. $\pi/2 - 1$
  4. Probability that $X^{2}+Y^{2}<0.5$
  5. None of the above.
asked in Probability by Loyal (6.8k points)
edited by | 403 views

2 Answers

+6 votes
Best answer

Area of square denotes the total probability, i. e, 1.
Area of circle denotes P(X + Y 2  ≤ 1)
Area of shaded region denotes the required probability, i.e, P(X 2+ Y 2 >1)


Area of shaded region=Area of square -Area of Circle
= 4 - 

= 4 ( 1 - /4)

If area of square corresponds to total probability, then
4 sq.unit=1
= 1 sq.unit=1/4
= 4(1-⊼/4) sq.unit=
=1-
/
which is the required probability.

answered by Boss (40.3k points)
selected by
+2 votes
(4-Pi)/4....is the answer
answered by Loyal (6.8k points)
0
4 - Pi is the area outside circle, you need to divide by total area that is 4 also.
+1
yeahhh man...thanks!


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