Question:
The random variable $\displaystyle T$ has the probability distribution given in the following table.
Attempt:
$\displaystyle E(T) = 4 , Var(T) = 19.6$
Where did I go wrong?
your definition of variance is wrong it's supposed to be:
$\displaystyle VAR(t) = \sum\limits_i {\left( {t_i - < t > } \right)^2 p(t_i )} $
or equivalently:
$\displaystyle
VAR(x) = \sum\limits_i {t_i ^2 p(t_i )} - \left[ {E(T)} \right]^2 = 19.6 - 16 = 3.6
$