SOLUTION: Explain whether the following statements are true or false. Give reasons. 1. E(1/X)=1/E(X) <---- E(X) represents the expected value 2. E[X-u(subscriptX)]^2 = [E(X-u(subscript

Algebra ->  Probability-and-statistics -> SOLUTION: Explain whether the following statements are true or false. Give reasons. 1. E(1/X)=1/E(X) <---- E(X) represents the expected value 2. E[X-u(subscriptX)]^2 = [E(X-u(subscript      Log On


   

Question 394859: Explain whether the following statements are true or false. Give reasons.
1. E(1/X)=1/E(X) <---- E(X) represents the expected value
2. E[X-u(subscriptX)]^2 = [E(X-u(subscriptX))]^2
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
1. E%281%2FX%29=1%2FE%28X%29. FALSE. Consider the pmf
X = 1 2 3
p(x) =0.2 0.3 0.5
Then E%28X%29+=+1%2A0.2+%2B+2%2A0.3++%2B3%2A0.5+=+23%2F10, but
E%281%2FX%29+=+1%2A0.2+%2B+%281%2F2%29%2A0.3++%2B%281%2F3%29%2A0.5+=+31%2F60.
Therefore E%281%2FX%29 is not equal to 1%2FE%28X%29.
2. E%28%28X-u%5Bx%5D%29%5E2%29+=+%28E%28X-u%5Bx%5D%29%29%5E2. FALSE.
The left side is Var(X), while the right side equal to 0, because