The total number of flaws (dents, scratches, paint blisters, etc) found on the various sets of doors installed on brand new minivans in an assembly plant is a random variable with the pdf:

The value of the pdf parameter, , depends on the door in question as follows: = 0.5 for the driver and front passenger doors; = 0.75 for the two bigger midsection passenger doors, and = 1.0 for the fifth, rear trunk/tailgate door. If the total number of flaws per completely assembled minivan is Y , obtain the pdf fY (y) and from it, compute the probability of assembling a minivan with more than a total number of 2 flaws on all its doors.