# Is ln(E(x^n)) equal to E(ln(x^n))

1. Jun 10, 2010

### xuej1112

is ln(E(x^n)) equal to E(ln(x^n)), if x is a continuous variable and x>=0???

Help me! Thanks!!!!!!!

2. Jun 10, 2010

### Gib Z

Re: help

This would more appropriately have been placed in the Calculus and Beyond homework help section, even if it isn't homework it is of that nature and level. General Math is more suited for general discussion of mathematical ideas.

Anyway, what is E? Is it the exponential function? How are the exponential function and natural logarithm related.

3. Jun 10, 2010

### xuej1112

Re: help

Sorry. E is the expectation

4. Jun 10, 2010

### Gib Z

Re: help

Oh ok. In that case, no it's not true. In fact, in general E(g(x)) is not equal to g(E(x)) which is due to the definition of E(x) as an integral with x as the integrand. This makes it inherently difficult for these nice properties to occur, as integrals don't have "nice" properties past linearity. So while E(aX+bY) = aE(X) + bE(Y), E(X^n) is not anything nice in terms of E(x).

5. Jun 10, 2010

### xuej1112

Re: help

thanks. if g is a concave function, can i say g(E(x))>=E(g(x)) ? (jensen's inequality)

6. Jun 10, 2010

### Gib Z

Re: help

It's the other way around, g(E(X)) is LESS or equal to E(g(X)), if g is convex (not concave).