Suppose that the overall profit , Y in dollars per day achieved by a particular

Question

Suppose that the overall profit , Y in dollars per day achieved by a particular network design can be expressed as Y=3X1-2X2,where X1 has mean 3.5 and standard deviation 2.0 and X2 has ean of 1.5 and standard deviation 0.5.Suppose further that X1 and X2 have correlation coefficient =0.4

a)what is the mean overall profit per day ?

b)what is the standard deviation of the overall profit per day?

c)if X1 and X2 are normally distributed ,what is the probability that the overall profit per day,Y, is less than $ 1.00?

Explanation / Answer

a) mean overall profit E(y)=3E(X1)-2*E(X2)=3*3.5-2*1.5=7.5

b)correlation coefficient r=0.4

standard deviation of the overall profit =SD(Y)=(32*Var(X1)+22*Var(X2)-2*3*2*r*SD(X1)*SD(X2))1/2

=(9*4+4*0.25-2*3*2*0.4*2*0.5)1/2 =5.6745

c)probability that the overall profit per day,Y, is less than $ 1.00 =P(X<1)=P(Z<(1-7.5)/5.6745)

=P(Z<-1.1455)=0.1260

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