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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, or leave immediately with probability 0.8. a) What is the expected time between successive bites

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Answer:

we will assume a variable X for time which is time between two successive bites and time until next bite.

X = (time between successive mosquito bites) = (time until the next mosquito bite).

According to the Bernoulli process, the bites occur parameter y = (0.5)(0.2) = 0.1.

X is a geometric random variable, so

E[X] = 1/p = 10

and

var(X) = (1 − p)/p^2 = (1 - 0.1)/0.1^2 = 0.9 / 0.01 = 90

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