Find the equation of this line. Simplify the fractions (Picture)
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Answer:
3
Step-by-step explanation:
The x-coordinate of the accident is a random variable of uniform distribution with range [-1.5,1.5]. The same can be said for the y-coordinate. However, |x| and |y| are also uniform variables with range [0,1.5], since we still have the same probability on every pair of intervals with the same lenght.
Note that |X| and |Y| are independent with each other, therefore E(|x|+|y|) = E(|x|) + E(|y|) = 2*E(|x|). The last equality holds because both x and y are identically distributed, then so are |x| and |y|.
E(|x|) =
Therefore, E(|x| + |y|) = 2 * 3/2 = 3.
I hope that works for you!