SOLUTION: Risk manager developed the following probability distribution for number of auto physical claims; # of claims Probability 12 .20 15

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Question 390747: Risk manager developed the following probability distribution for number of auto physical claims;
# of claims Probability
12 .20
15 .60
18 .20
The mean of probability distribution is 15 claims. What is the standard deviation?
Please explain
the process as well.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
mu+=+15 ===> sigma%5E2+=+E%28X%5E2%29+-+mu%5E2, or
. This is the variance of the distribution. Its square root is the standard deviation, or sigma+=+%283sqrt%2810%29%29%2F5+=+1.8974+, to 4 decimal places.
E%28X%5E2%29+ means expectation, or the mean of the squares of the random variables. It does NOT mean the sum of squares. After squaring each random variable value, you have to multiply each squared value with its corresponding probability. Please read entirely the solution to the problem.