SOA Exam P Sample Question 443
Study guide: Exam P-1
A continuous random variable, X, has density function f(x) where
f(x) = \begin{cases}
\dfrac{x-1}{4}, & \text{for } 1 < x < 3 \\[4pt]
\dfrac{5-x}{4}, & \text{for } 3 \leq x < 5 \\[4pt]
0, & \text{otherwise.}
\end{cases}Determine which of the following expressions equals E\bigl(|X-2|\bigr).
- A)
\dfrac{1}{4}\int_1^2 (2-x)(x-1)\,dx + \dfrac{1}{4}\int_2^3 (x-2)(x-1)\,dx + \dfrac{1}{4}\int_3^5 (2-x)(5-x)\,dx - B)
\dfrac{1}{4}\int_1^3 (2-x)(x-1)\,dx + \dfrac{1}{4}\int_3^5 (x-2)(5-x)\,dx - C)
\dfrac{1}{4}\int_1^2 (x-2)(x-1)\,dx + \dfrac{1}{4}\int_2^3 (2-x)(x-1)\,dx + \dfrac{1}{4}\int_3^5 (2-x)(5-x)\,dx - D)
\dfrac{1}{4}\int_1^3 (x-2)(x-1)\,dx + \dfrac{1}{4}\int_3^5 (x-2)(5-x)\,dx - E)
\dfrac{1}{4}\int_1^2 (2-x)(x-1)\,dx + \dfrac{1}{4}\int_2^3 (x-2)(x-1)\,dx + \dfrac{1}{4}\int_3^5 (x-2)(5-x)\,dx
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