Question

You have 7 pounds of a product in stock, and the demand (D) for the item is a continuous random variable with the following density function:

f(d) =

0.2, if 5 ≤ d ≤ 10
0, otherwise
(a) Calculate the probability that the stock can meet the demand.

(b) Calculate the expected weight of items sold.

(c) Calculate the variance of the weight of the items sold.

(d) If this product is sold at the price of $4 per pound, calculate the expected total revenue.

(e) Continuing from part (d), calculate the variance of the total revenue.

Answer 1

The probability that the stock can meet the demand is 1. The expected weight of items sold cannot be calculated without the weight of each item.

Step-by-step explanation:

(a) Probability that the stock can meet the demand:

To calculate the probability that the stock can meet the demand, we need to find the area under the density curve that represents the demand function. In this case, the demand function is represented by a rectangle from 5 to 10 with a height of 0.2. The area of this rectangle is the probability that the demand falls within this range.

The width of the rectangle is 10 - 5 = 5, and the height is 0.2. Therefore, the area is 5 * 0.2 = 1. So, the probability that the stock can meet the demand is 1.

(b) Expected weight of items sold:

The expected weight of items sold can be calculated by multiplying the demand by the weight of each item. The weight of each item is not provided in the question, so this calculation cannot be done without that information.