A chemical supply company ships a certain solvent in 10-gallon drums. Let X represent the number of drums ordered by a randomly chosen customer. Assume X has the following probability mass function:
a. Find the mean number of drums ordered.
b. Find the variance of the number of drums ordered.
c. Find the standard deviation of the number of drums ordered.
d. Let Y be the number of gallons ordered. Find the probability mass function of Y.
e. Find the mean number of gallons ordered.
f. Find the variance of the number of gallons ordered.
g. Find the standard deviation of the number of gallons ordered.
a) 
= 1(0.4) + 2(0.2) + 3(0.2) + 4(0.1) + 5(0.1) = 2.3
(b) 
(c) 
(d) Y = 10X. Therefore the probability density function is as follows.
(e) 
= 10(0.4) + 20(0.2) + 30(0.2) + 40(0.1) + 50(0.1) = 23
(f) 
(g) 
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