Question

Suppose that the number of defects in a 1200-foot roll

of magnetic recording tape has a Poisson distribution for

which the value of the mean θ is unknown and that the

prior distribution of θ is the gamma distribution with parameters

α = 3 and β = 1. When five rolls of this tape are

selected at random and inspected, the numbers of defects

found on the rolls are 2, 2, 6, 0, and 3. Determine the posterior

distribution of θ.

Answer 1