Actuarial Notes

SOA Exam P Sample Question 565

Study guide: Exam P-1

The proportion of cotton plants on a large farm infested with boll weevils is modeled by a continuous random variable with probability density function

f(x) = \begin{cases}
20x^3(1-x), & \text{for } 0 \leq x \leq 1 \\
0, & \text{otherwise.}
\end{cases}

Calculate the standard deviation of the proportion of cotton plants on the farm that are infested with boll weevils.

  • A) 0.032
  • B) 0.178
  • C) 0.476
  • D) 0.690
  • E) 0.959

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