SOLUTION: 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 pr

Algebra ->  Probability-and-statistics -> SOLUTION: 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 pr      Log On


   

Question 1022893: 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:

x 1 2 3 4 5
p(x) 0.36 0.19 0.17 0.06 0.22

Find the variance of the number of drums ordered.

The variance of number of drums ordered =
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
We make use of the formula Var%28X%29+=+E%28X%5E2%29+-+%28E%28X%29%29%5E2.
To find E%28X%5E2%29, we find pmf of X%5E2:
X%5E2 1 4 9 16 25
p(X%5E2%29) 0.36 0.19 0.17 0.06 0.22
which is identical to the pmf of X.
==> E%28X%5E2%29+=+1%2A0.36%2B+4%2A0.19+%2B+9%2A0.17+%2B+16%2A0.06+%2B+25%2A0.22+=+9.11
Now E(X) = 0.36 + 2*0.19 + 3*0.17 + 4*0.06 + 5*0.22 = 2.59
==> Var%28X%29+=+9.11+-+2.59%5E2+=+2.4019