New product inventory management. Estimating the demand for a new product during lead-time is important for product inventory management. The International Journal of Production Economics (August 2008) demonstrated that the demand distribution for a new product during lead-time may be best modeled by the uniform distribution. The only parameters that need to be known are the minimum and maximum values of demand. In a numerical example presented in the article, the maximum demand for a new product was estimated to be 100 units. Obviously, the minimum demand is 0 units. Assume that demand, x, has a uniform distribution.

a. Give a formula for the probability density function for x.

b. Find the mean and variance of x.

c. Find the probability that the demand for the new product is less than 30 units.