Reference no: EM131084695
An ice cream company orders supplies by fax. Depending on the size of the order, a fax can be either
1 page for a short order,
2 pages for a long order
The company has three different suppliers:
The vanilla supplier is 20 miles away.
The chocolate supplier is 100 miles away.
The strawberry supplier is 300 miles away.
An experiment consists of monitoring an order and observing N, the number of pages, and D, the distance the order is transmitted.
The following probability model describes the experiment:
(a) What is the joint PMF PN,D(n, d) of the number of pages and the distance?
(b) What is E[D], the expected distance of an order?
(c) Find PD|N (d|2), the conditional PMF of the distance when the order requires 2 pages.
(d) Write E[D|N = 2], the expected distance given that the order requires 2 pages.
(e) Are the random variables D and N independent?
(f) The price per page of sending a fax is one cent per mile transmitted. C cents is the price of one fax. What is E[C], the expected price of one fax?
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