- #1
rosh300
- 17
- 0
Homework Statement
find the mean and varince of Log(X) Where X~U[1,0] (X is continuous Random variable)
Homework Equations
[tex] \mathbb{E}(X) = \int_{-\infity}^{\infity}{x f_X(x)} dx [/tex]
[tex] \mathbb{E}(X^2) = \int_{-\infity}^{\infity}{x^2 f_X(x)} dx [/tex]
[tex] Var(X) = \mathbb{E}(X^2) - (\mathbb{E}(X))^2 [/tex]
The Attempt at a Solution
[tex] \mathbb{E}[log(x)] = \int_0^1{xlog(x)} = \frac{-1}{4} [/tex]
[tex] \mathbb{E}[log(x)^2] = \int_0^1{x^2log(x)} = \frac{-1}{9} [/tex]
[tex] Var(X) = \mathbb{E}[log(x)^2] - \mathbb{E}[log(x)]^2 = \frac{-25}{144} [/tex]
but i know variance can't be negative