Expected value and variance?

The following probability distribution of number of children per family was provided by the european community of vital statistics





x (number of children) %


0 - 12


1 - 16


2 - 25


3 - 19


4 - 14


5 - 4


6 - 3


7 - 2


8 - 2


9 - 2


10 - 1





Find the expected value of number of children and the variance





I know that you take the sum of (x multiplied by Pr(x)) but I dont know how to get the expected value. Sorry the spacing is so messed up. The first number is the x value the number after the dash is the percentage. Thank you!

Expected value and variance?
This: "I know that you take the sum of (x multiplied by Pr(x))"


contradicts this: "I don't know how to get the expected value."





That IS how you get the expected value: ∑x*P(x). So letting the number of children be x, we find:





E(x) = 0*.12 + 1*.16 + 2*.25 + 3*.19 + 4*.14 + 5*.04 + 6*.03 + 7*.02 + 8*.02 + 9*.02 + 10*.01 = 2.75





Now, the variance is defined as E((x-E(x))²), or for faster computation, we may use the equivalent formula E(x²) - E(x)². We already know E(x), so to find E(x²), we simply take ∑x²*P(x), which is:





E(x²) = 0*.12 + 1*.16 + 4*.25 + 9*.19 + 16*.14 + 25*.04 + 36*.03 + 49*.02 + 64*.02 + 81*.02 + 100*.01 = 12.07





So the variance is E(x²) - E(x)² = 12.07 - 2.75² = 4.5075.
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