[R] Looking for simpler solution to probabilistic question

[Rainer M Krug]

Hi

I have two processes which take with a certain probability (p1 and p2) x 
number of years to complete (age1 and age2). As soon as thge first 
process is completed, the second one begins. I want to calculate the 
time it takes for the both processes to be completed.

I have the following script which gives me the answer, butI think there 
must be a more elegant way of doing the calculations between the #####

Any ideas welcom,

Rainer


age1 <- 1:20
p1 <- dnorm(age1,10,2)

age2 <- 10:30
p2 <- dnorm(age2,15,1)

######
age <- matrix(age1, ncol=length(age1), nrow=length(age2), byrow=TRUE) + age2

p <- matrix(p1, ncol=length(p1), nrow=length(p2), byrow=TRUE) + p2
p <- as.numeric(tapply(p, age, sum))
p <- p / sum(p)
#####

age <- sort(unique(as.numeric(age)))

plot(age, p)

lines(age1, p1)
lines(age2, p2)