# Example 2(a) from end of Sec. 5.2 notes:


f.t<-function(t){
.0625*exp(-.0625*t)*(.05/(.05-.0625))*(.1/(.1-.0625)) +
.05*exp(-.05*t)*(.0625/(.0625-.05))*(.1/(.1-.05)) +
.1*exp(-.1*t)*(.0625/(.0625-.1))*(.05/(.05-.1))
}

integrate(f.t, lower=0, upper=30)

# Example 2(b) from end of Sec. 5.2 notes:

fY.t<-function(t){
( .0625*exp(-.0625*t) )*0.2 +

( .0625*exp(-.0625*t)*(.05/(.05-.0625)) +
.05*exp(-.05*t)*(.0625/(.0625-.05)) )*0.3 +

( .0625*exp(-.0625*t)*(.05/(.05-.0625))*(.1/(.1-.0625)) +
.05*exp(-.05*t)*(.0625/(.0625-.05))*(.1/(.1-.05)) +
.1*exp(-.1*t)*(.0625/(.0625-.1))*(.05/(.05-.1)) )*0.5
}

integrate(fY.t, lower=0, upper=30)