Problem \# 01: The joint distribution of amount of pollutant emitted from a smokestack without a cleaning device (Y
1
) and similar smokestack with a cleaning device (Y
2
) is given below f(y
1
,y
2
)={
1
0
for 0≤y
1
≤2,0≤y
2
≤1,2y
2
≤y
1
elsewhere
(a) Find the marginal density function of Y
1
and Y
2
. Then Find E(Y
1
−Y
2
). (b) The reduction in amount of pollutant due to the cleaning device is given by U=Y
1
−Y
2
. Find the probability density function of U. Compute E(U) and compare the result with part (a). Problem \# 01: The joint distribution of amount of pollutant emitted from a smokestack without a cleaning device (Y
1
) and similar smokestack with a cleaning device (Y
2
) is given below f(y
1
,y
2
)={
1
0
for 0≤y
1
≤2,0≤y
2
≤1,2y
2
≤y
1
elsewhere
(a) Find the marginal density function of Y
1
and Y
2
. Then Find E(Y
1
−Y
2
). (b) The reduction in amount of pollutant due to the cleaning device is given by U=Y
1
−Y
2
. Find the probability density function of U. Compute E(U) and compare the result with part (a).