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_X(x)= * x^{(+ 1)};0< x <1; > 0

0Otherwise

where x is the proportion of the task completed. The engineer will take a sample of 4 independent projects and record the proportion of the tasks completed in time.

1. What is the joint density of the sample, f(x₁, x₂, x₃, x₄)?
2. What is the maximum likelihood estimate of.