The probability density function of the weight of packages

Solution 48E

Step1 of 4:

Let us consider a random variable X it presents the weight of packages delivered by a post office.

Then probability density function of X is:

for

Here our goal is:

a). We need to determine the mean and variance of weight.

b). We need to find the average shipping cost of a package. When the shipping cost is $2.50 per pound.

c). We need to determine the probability that the weight of a package exceeds 50 pounds.

Step2 of 4:

a).

The mean of X is given by: