An urn contains 7 red and 11 white balls. Draw one ball at random from the urn. Let X = 1 if a red ball is drawn, and let X = 0 if a white ball is drawn. Give the pmf, mean, and variance of X.
I got the pmf and the mean correct, however my variance answer is not matching up with the correct answer which is 77/324. Is this answer correct?
The formula I am using is x^2 f(x) - mean^2. Thanks in advance.
Yes, $\mathsf {Var}(X) = \frac {77}{324}$.
Which is indeed obtained by $\mathsf {Var}(X)~=~ 1^2{\cdot}\mathsf P(X=1)-(1{\cdot}\mathsf P(X=1))^2$.