I know I'm supposed to use the the Standard Normal Cumulative distribution function. But I can't seem to get everything I need.
Let $X$ be a random variable with $P(X=-1)=P(X=0)=0.25$ and $P(X=1)=0.5$ Let $S$ be the sum of $25$ independent variables with the same distribution as $X$.
Find $P(S<0)$.
So I was able to find $μ$ by finding $E(X)= \sum_{i=-1}^{1} x_ip(x_i)= 0.25$ however I'm not sure how to find $S.D.(X)$ and then bring those two variables in terms of $S$. i.e. $E(X)$ and $S.D.(S)$.
I know to find $S.D.(X)$ I need to first find the variance of $X$ i.e. $\operatorname{Var}(X)=E(X^2)+[E(X)]^2$ and then take the square root but I'm not sure where to go from there...