6.50 The total sustained load on the concrete footing of a planned building is the sum of the deadload plus the occupancy load. Suppose the dead load X1 has a gamma distribution with and , while the occupancy load X2 has a gamma distribution with and .

(Units are in kips, or thousands of pounds.)

a Find the mean, variance, and probability density function of the total sustained load on the footing.

b Find a value for the sustained load that should be exceeded only with probability less than 116.