Thread: variance relationship of bernouilli rv

I am having problems understanding an explanation.

So we have constructed a random variable Y and Z which are both identical and independently distributed Bernoulli random variables with probability of 1/2. Now we create a new random variable X such that X=YZ. X is thus a Bernoulli rv with probability 1/4. Apparently its supposed to be obvious that Var[X|Y=1] = Var[Z], but I don't see why. Can anyone explain this step?

Originally Posted by jimmianlin

I am having problems understanding an explanation.

So we have constructed a random variable Y and Z which are both identical and independently distributed Bernoulli random variables with probability of 1/2. Now we create a new random variable X such that X=YZ. X is thus a Bernoulli rv with probability 1/4. Apparently its supposed to be obvious that Var[X|Y=1] = Var[Z], but I don't see why. Can anyone explain this step?

Forget about the variance and all the Bernoulli stuff....
IF Y=1 then X=YZ=(1)(Z)=Z