1.3 You are visiting the rainforest, but unfortunately your insect repellent has run out. 1. As...

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1.3 You are visiting the rainforest, but unfortunately your insect repellent has run out. 1. As a result, at each second, a mosquito lands on your neck with probability 0.2. (a) What's the PMF for the time until the first mosquito lands on you? (b) What's the expected time until the first mosquito lands on you? (c) What if you weren't bitten for the first ten seconds what would be the expected - time until the first mosquito lands on you (from time t = 10)? 2. Instead, imagine the rainforest had only one mosquito, which arrived in the following way: the time of arrival is exponentially distributed with X = 0.2. (a) What's the expected time until the first mosquito lands on you? (b) What if you weren't bitten for the first ten seconds what would be the expected time until the first mosquito lands on you (from time t=10)? 1.3 You are visiting the rainforest, but unfortunately your insect repellent has run out. 1. As a result, at each second, a mosquito lands on your neck with probability 0.2. (a) What's the PMF for the time until the first mosquito lands on you? (b) What's the expected time until the first mosquito lands on you? (c) What if you weren't bitten for the first ten seconds what would be the expected - time until the first mosquito lands on you (from time t = 10)? 2. Instead, imagine the rainforest had only one mosquito, which arrived in the following way: the time of arrival is exponentially distributed with X = 0.2. (a) What's the expected time until the first mosquito lands on you? (b) What if you weren't bitten for the first ten seconds what would be the expected time until the first mosquito lands on you (from time t=10)?