Reference no: EM132643336

This question should be carried out in R. You must include your R code in your answers. Hint: You can use the R function integrate for many of the following questions.

Let X denote the October demand (measured in 1000's of units), for a particular product. Historical demand figures suggest that a suitable probability density function for X is

(a) = (2/3) r20 otherwise

(a) Using R, create a plot of the probability density function (). Your plot should have adequate labels and an appropriately chosen scale for the horizontal axis.

(b) Using the R function integrate, show that (x) dx = 1. In doing so, and by noting that (x) > 0 for all a, you will therefore have shown that is a valid probability density function, (c) Compute the mean of X: i. by using the R function integrate;

(d) Suppose that the company manufacturing the product in question will order 1100 units for the next October period. What is the probability that demand will exceed supply? In other words, what is P(X > 1.1)? (e) Unless the company sells at least 85 units of the item in question each October, it may be forced to file for bankruptcy. Compute the probability that the company exceeds this minimum amount of 85 units sold, while also having enough stock on hand to meet demand, having ordered 1100 units.