Question

4. The density of eggs laid by an insect in a given time period has a Poisson distribution with a mean of 8.2 eggs per cubic centimetre. The number of eggs that survive to their larval stage is given by $L(j) = 3 \cdot (2 - r^j)$, where $j$ is the number of eggs per cubic centimetre laid and $r$ is a constant where $0 < r < 1$. (a) [5 pts] Determine the probability that the density of eggs laid is greater than the mean. (Determine a numerical estimate of this value.) (b) [5 pts] Samples are made, and it is determined that the density of larvae is at least four per cubic centimetre. Determine the probability that the density of eggs laid is greater than the mean. (c) [5 pts] Determine the expected number of eggs to reach their larval stage.

          4. The density of eggs laid by an insect in a given time period has a Poisson distribution with
a mean of 8.2 eggs per cubic centimetre. The number of eggs that survive to their larval
stage is given by
$L(j) = 3 \cdot (2 - r^j)$, 
where $j$ is the number of eggs per cubic centimetre laid and $r$ is a constant where $0 < r < 1$.
(a) [5 pts] Determine the probability that the density of eggs laid is greater than the mean.
(Determine a numerical estimate of this value.)
(b) [5 pts] Samples are made, and it is determined that the density of larvae is at least
four per cubic centimetre. Determine the probability that the density of eggs laid is
greater than the mean.
(c) [5 pts] Determine the expected number of eggs to reach their larval stage.

4. The density of eggs laid by an insect in a given time period has a Poisson distribution with
a mean of 8.2 eggs per cubic centimetre. The number of eggs that survive to their larval
stage is given by
L(j) = 3 · (2 - r^j),
where j is the number of eggs per cubic centimetre laid and r is a constant where 0 < r < 1.
(a) [5 pts] Determine the probability that the density of eggs laid is greater than the mean.
(Determine a numerical estimate of this value.)
(b) [5 pts] Samples are made, and it is determined that the density of larvae is at least
four per cubic centimetre. Determine the probability that the density of eggs laid is
greater than the mean.
(c) [5 pts] Determine the expected number of eggs to reach their larval stage.

Added by Kristen J.

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