f(x) = 1/ pi (1+x2), where x R Find the mean of the random variable X with this probability function Solution E(x) = int x.f(x) dx = int x/(1+x2) dx = 1/2 ln(x2 +1) (x from -a to a when a -> ) = 1/2 (ln(1+a^2) - ln(1+a^2)) = 0 Therefore the mean is zero: E(x) = 0.

1. f(x) = 1/ pi (1+x2), where x R Find the mean of the random variable X with this probability
function
Solution
E(x) = int x.f(x) dx = int x/(1+x2) dx = 1/2 ln(x2 +1) (x from -a to a when a -> ) =
1/2 (ln(1+a^2) - ln(1+a^2)) = 0
Therefore the mean is zero:
E(x) = 0