Determine the 50% equal-tailed credible interval for based on the posterior distribution f(|x 1 , x

Determine the 50% equal-tailed credible interval for θ based on the posterior distribution f(θ|x₁, x₂) = (1-(θ-x₂))(θ-x₁).

 Examine the frequentist properties of this credible interval, either by simulation1 or analytically, by determining:

 

(1) the average length of this 50% credible interval, and

 

(2) the coverage probability of this 50% credible interval.