exercise:F65c4c4362: Difference between revisions

Latest revision as of 22:19, 7 May 2023

Automobile claim amounts are modeled by a uniform distribution on the interval [0, 10,000]. Actuary A reports [math]X[/math], the claim amount divided by 1000. Actuary B reports [math]Y[/math], which is [math]X[/math] rounded to the nearest integer from 0 to 10.

Calculate the absolute value of the difference between the 4^th moment of [math]X[/math] and the 4^th moment of [math]Y[/math].

0
33
296
303
533

@@ Line 1: / Line 1: @@
-'''Solution: B'''
+Automobile claim amounts are modeled by a uniform distribution on the interval [0, 10,000]. Actuary A reports <math>X</math>, the claim amount divided by 1000. Actuary B reports <math>Y</math>, which is <math>X</math> rounded to the nearest integer from 0 to 10.
-The fourth moment of <math>X</math> is
+Calculate the absolute value of the difference between the 4<sup>th</sup> moment of <math>X</math> and the 4<sup>th</sup> moment of <math>Y</math>.
-<math display = "block">
+<ul class="mw-excansopts">
-\int_0^{10} \frac{x^4}{10} dx = \frac{x^5}{50} \Big |_0^{10} = 2000.
+<li>0</li>
-</math>
+<li>33</li>
+<li>296</li>
-The <math>Y</math> probabilities are 1/20 for <math>Y = 0 </math> and 10, and 1/10 for <math>Y = 1,2, \ldots, 9 </math>.
+<li>303</li>
+<li>533</li>
-<math display = "block">
+</ul>
-\operatorname{E}[Y^4] = (1^4 + 2^4 + \cdots + 9^4)/10 + 10^4/20 = 2033.3.
-</math>
-The absolute value of the difference is 33.3.
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