
  1.  Emma is performing an experiment that requires individual handling of some animals. The sizes of the animals are lognormally distributed: The natural logarithms of their sizes has a normal distribution with mean 3 and standard deviation 0.4. The time (in minutes) it takes to handle each animal is given by

10 + s · 1.5 + eε for animals with s ≤ 20 20 + s · 0.8 + eε for animals with s > 20

where ε is a random variable that is normally distributed with expectation 1 and variance 0.3.

For a randomly picked animal, what is the (approximate) probability that it can be handled in less than 30 minutes?

We can solve this exercise using simulation, as follows: Simulate a vector S with the sizes of 10000 animals, by using the rnorm function and the “exp” function. Then, compute a vector Time of length 10000 with the times it takes to handle each of these 10000 animals: Remember that to separate between the two cases, you can use notation like for example “Time[S < 20]”. The random component eε can be added by combining the “exp” function with the “rnorm” function. Finally, you can find the proportion of simulated values below 30. Re-do the computations a couple of times to get an idea of the variability of the result.

s <- c(10000)
S <- exp(rnorm(s, 3, 0.4)) [1]# vector 10000, mean, sd
Time <- 10+S*1.5 [1] # 10 + s · 1.5 + eε for animals with s ≤ 20
time <- 20+S*0.8 [1] #   20 + s · 0.8 + eε for animals with s > 20

can't get any further and i can't really find a good help page to solve the code.
can you help me?
Lotta

------------------------------------------------------------------------------------
Eva-Lotta Blom PhD student
Dept. of BioEnv . Tjärnö
University of Gothenburg
452 96 Strömstad
Sweden







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