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Statistics Question Involving Variance and Expectation?
Define a random variable X so that:
E[(X-1)^2]=10
E[(X-2)^2]=6
Find E(X) and the variance of X
Yeah...I've made it through the rest of the chapter no problem but this one is murdering me, anyone know what to do?
1 Answer
- LeonardLv 77 years agoFavorite Answer
E[(X^2 -2X +1]=E(X^2) -2E(X) +1 =10. (1)
E[(X^2 -4X +4]=E(X^2) -4E(X) +4 =6. (2)
Subtracting (2) from (1), 2E(X) -3=4, and E(X)=7/2=3.5.
using (1), E(X^2)=2(7/2)+9=16.
Var(X)=E(X^2) - E(X)^2=16-(3.5)^2=3.75.
