Stringerbelltx:
A woman in a highland village in the Andes knits sweaters and sells them for export. She also takes care of her family and helps farm the family land; therefore, the amount of time she can devote to knitting is random. The probability distribution of the number of sweaters she can produce per month is as follows:
Number of sweaters (x) 2 3 4 5 6 7
Px(X) .1 .1 .2 .3 .2 .1
a. What is the expected number of sweaters per month she manufactures?
b. What is the variance of the number of sweaters per month she manufactures?
c. The exporter pays $12 for each sweater. The woman pays $2 per sweater for yarn. She also pays $3 per month to send the sweaters to the exporter (this is the shipping cost regardless of the number of sweaters shipped). Give profit from knitting sweaters as a function of the number of sweaters knitted.
d. What are expected profits and the variance of profits?