Chapter 5.2, Problem 7Q

An engineer is creating a project scheduling program and recognizes that the tasks making up the project are not always completed on time. However, the completion proportion tends to be fairly high. To reflect this condition, he uses the pdf

$f_Y\left(y;\theta \right)=\theta y^{\theta -1},0\le y\le 1$, and $0<\theta$ where $y$ is the proportion of the task completed. Suppose that in his previous project, the proportions of tasks completed were 0.77, 0.82, 0.92, 0.94, and 0.98. Estimate $\theta$.