SOLUTION: Dave gave a six question quiz to his Statistics students. The students were talented, and no one scored below a 4. Half the students scored 4, 40% scored 5, and 10% scored 6. Co

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Question 1026509: Dave gave a six question quiz to his Statistics students. The students were talented, and no one scored below a 4. Half the students scored 4, 40% scored 5, and 10% scored 6. Compute the variance of this distribution (round answer to one decimal place).
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Let X = random variable for the score
PMF:
X=x 1 2 3 4 5 6
p(X=x) 0 0 0 0.50 0.40 0.10
==> E(X) = 1*0+2*0+3*0+4*0.50+ 5*0.40 +6*0.10 = 2+2+0.6 = 4.6, the mean of the distribution.
PMF of X%5E2
X%5E2+=+x%5E2 1 4 9 16 25 36
p(X%5E2+=+x%5E2) 0 0 0 0.50 0.40 0.10
==> ,
==>+Var%28X%29+=+E%28X%5E2%29+-+%28E%28X%29%29%5E2+=+21.6+-+4.6%5E2+=+0.44