Let theta denote the average number of defects per 100 feet of a certain type of magnetic tape. suppose that the value of the mean theta is unknown and the prior distribution of theta is a gamma distribution with parameters alpha=2 and beta=10. when a 1200 foot roll of this tape is inspected, exactly four defects are found. determine the posterior distribution of theta.

i'm pretty sure the posterior is a gamma function i just need to figure out alpha and beta. do i multiply by 12...?