Question

You are visiting the rainforest, but unfortunately your insect repellent ran out. As a result, at each minute, with probability 0.5, one mosquito lands on your neck, and with probability 0.5, no mosquito lands. If a mosquito lands, it will bite you immediately with probability 0.2, and it never bother you with probability 0.8, independently of other mosquitoes.

a) What is the expected time between successive bites?

b) Assume that each mosquito that lands on your neck bites you no more than once. If the blood it drains from your with a bite is a discrete uniform random variable with value in {1,2,3,4} (in ml), then what are the expected value and variance of your blood loss from this mosquito?

Answer 1