bernoulli trials

[hoffmann]

say you perform one bernoulli experiment where outcome X = 0 and X=1 are failure and success, respectively. then you have P(X=0) = 1-p and P(X=1) = p.

what if you expand this to two bernoulli experiments? only 1/4 cases would be successful, so you would have:

P(X=1) = p^2
E(X) = p^2
Var(X) = ?

i'm hung up on how to calculate Var(X). any thoughts?

[Office_Shredder]

1/4 cases are successful if you define success to be two consecutive trials in a row succeed. In this case you just have a single Bernoulli trial with probability of success p2. So just take the formula for the variance of a Bernoulli trial and plug in p2