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, or leave immediately with probability 0.8.

a) What is the expected time between successive bites?

b) Now we look at each mosquito that lands on your neck, and assume that it 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

Answer:

Given that:

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?

A mosquito lands on your neck with probability = 0.5

It will bite you with probability = 0.2

Required to find expected the time between successive bites.

Probability of mosquito bit/sec = 0.5*0.2

Probability of mosquito bit/sec (p) = 0.1

Expected value

b)  Now we look at each mosquito that lands on your neck, and assume that it 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?

The blood chains from every bit is a discrete uniform random variable(Y)

Y	1	2	3	4
P(Y=y)	0.25	0.25	0.25	0.25