The lifetime (in days) of a certain type of organisms is considered to be a random variable Y with density fy(y) - 200 (20 - y) for 0 .) for r ER. Note that, in the current context, this can be interpreted as the probability of an organism surviving beyond time x. Show that the survival function of Y is 1 for y 20. (C) [4 marks] Justify that, in the current context, E(Y) = Sy (y ) dy , and make use of this result to obtain the life expectancy of these organisms