Revision as of 22:16, 7 May 2023 by Admin (Created page with "'''Solution: B''' The fourth moment of <math>X</math> is <math display = "block"> \int_0^{10} \frac{x^4}{10} dx = \frac{x^5}{50} \Big |_0^{10} = 2000. </math> The <math>Y</...")
ABy Admin
May 07'23
Exercise
Solution: B
The fourth moment of [math]X[/math] is
[[math]]
\int_0^{10} \frac{x^4}{10} dx = \frac{x^5}{50} \Big |_0^{10} = 2000.
[[/math]]
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].
[[math]]
\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.
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
May 07'23
Solution: B
The fourth moment of [math]X[/math] is
[[math]]
\int_0^{10} \frac{x^4}{10} dx = \frac{x^5}{50} \Big |_0^{10} = 2000.
[[/math]]
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].
[[math]]
\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.
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.