here is a species of goat parasite whose larval stage lasts

here is a species of goat parasite, whose larval stage lasts for 6 days and who never live longer than 16 days total. Thus, considering a parasite of this species that reaches adulthood, the lifespan is always somewhere between 6 and 16 days. A certain authority (it happens to be the same as the 2nd guy above) claims that the lifespan of these goat parasites is distributed according to the beta distribution with parameters = 3, = 3, A = 6, and B = 16. Assuming that this guy is correct, answer the following. (This problem is going to take a lot of work. Be sure to give yourself plenty of time.) a.) State (in simplified form as much as possible) the formula for the probability density function of this distribution. b.) State (again in as simplified a form as you can) the formula for the cumulative distribution function of this distribution. c.) What is the average lifespan of these goat parasites? d.) What is the standard deviation in lifespan of these? e.) What is the median lifespan of these? f.) What is the probability that a given goat parasite will live for somewhere between 8 and 12 days?

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