During an eighthour shift the proportion of time Y that a sh

During an eight-hour shift, the proportion of time Y that a sheet-metal stamping machine is down for maintenance or repairs has a beta distribution with alpha = 1 and beta = 2 = 2. Find the expected proportion of time the machine will be down for maintenance or repairs. Find the variance of the proportion of time the machine will be down for maintenance or repairs.

Solution

Expected proportion of time the machine will be down for maintenance or repairs = alpha/ ( alpha+beta) = 1/3...

variance = alpha*beta / [ (alpha+ beta)^2 * (alpha+beta+1) ] = 2 / ( 9 * 4 ) = 1 / 36.........