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Automobile claim amounts are modeled by a uniform distribution on the interval [0, 10,000]. Actuary A reports X, the claim amount divided by 1000. Actuary B reports Y, which is X rounded to the nearest integer from 0 to 10. Calculate the absolute value of the difference between the 4th moment of X and the 4th moment of Y.

Part of Solution: The Y probabilities are 1/20 for Y = 0 and 10, and 1/10 for Y = 1,2,…,9

Can someone explain with calculations and formulas on how they got "1/20 for Y = 0 and 10, and 1/10 for Y = 1,2,…,9" for this part?

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    $\begingroup$ What $Y$ do you get for values of $X$ between $0$ and $\frac12$? What happens to values of $X$ between $\frac12$ and $1\frac12$? $\endgroup$
    – Glen_b
    Nov 27, 2017 at 3:54
  • $\begingroup$ Please add the [self-study] tag & read its wiki. $\endgroup$ Nov 27, 2017 at 8:48

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$$\Pr(Y=0)=\Pr(X<0.5)=0.5/10=1/20$$ and similarly for the rest of the values of $Y$.

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