The environmental engineer in problem 6 is concerned with catching fish. Again, assume the capture of fish is a binomial experiment and the probability any fish is parasitized is 0.10. Let X be the number of fish required to be caught to have 3 parasitized fish.
a) What is the probability that X =15?
b) What is E(X)?
c) What is the standard deviation of X?
d) Suppose the environmental engineer is concerned with costs. Suppose it costs $1000 just to start fishing, and it costs $500 for every fish caught whether the fish is parasitized or not. What is the expected cost? Assume X is the random variable of interest.
e) Assuming the same costs as in part d, what is the standard deviation of the cost? Again, assume X is the random variable of interest.