Assignment | Professional Writing Services
January 13th, 2020
Q. 1 Darts revisited
Consider a circular dart board with radius one. I throw a dart at the board and record
the (X,Y) position (note that the dart will land in the board, and (X,Y) are uniformly distributed on the
board).
1. Find the marginal distribution of X.
2. Let R2 = X2 +Y2
(i.e. R is the distance from the center)
Find E[R] and E[R2]. (Please note that E[X]2 6=E[X2]
unless X is a constant random variable).
3. Let B∼Uniform[0,1]
and independent of R. Calculate
E[(R−B)2]
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