Question

At a computer store, the annual demand for a particular software is a discrete random variable, X. The store owner orders four software copies at $ 10 per copy and charges customers $ 35 per copy. At the end of the year, the software is obsolete and the owner loses the investment on unsold copies. The pmf of X is given by the following table. X 0 p(x) | 0.1 1 0.3 2 0.3 3 0.2 4 0.1 • Find E(X) and V(X) • Express the owner's net profit Y as a function of X and find E(Y) and V(Y)

Answer 1

Solution:

The E(X) and V(X) are given below:

p(x) 0.1 0.3 0.3 0.3 Xp(X) p(X)(X - Mean) 0.361 0.243 0.6 0.6 0.242 0.4 0.441 Mean= Xp(X) = 1.9 Ep(X)(X - Mean)' = 1.29 0.003 0.2 0.1 :: E(X)= Mean=1.9 V(X)={p(X)(X - Mean) = 1.29

Ply) Yp(y) 0.1 0.3 -1.5 0.3 p(y)(Y - Mean)? 442.225 297.675 3.675 296.45 540.225 Ep(y)(Y - Mean)' = 1580.25 0.2 13 30 65 100 Mean = Yp(y) =26.5 :: E(Y) = Mean = 26.5 V(Y)=p(y)(v - Mean)? = 1580.25 0.1