Suppose that the number of eggs laid by a certain insect

Solution 153SE

Step1 of 3:

Let us consider a random variable Y it presents the the number of eggs laid by a certain insect.

Here Y follows poisson distribution with parameter . The probability that any one egg hatches is p. and assume that the eggs hatch independently of one another.

Here our goal is:

a). We need to find the expected value of Y, the total number of eggs that hatch.

b). We need to find the variance of Y.

Step2 of 3:

a).

We know that the probability mass function of poisson distribution is:

y = 0,1,...,n.

Let N denote the number of eggs the insect lays, define:

Here Nand then Y

Now,