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Math Help - variance relationship of bernouilli rv

  1. #1
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    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?
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  2. #2
    MHF Contributor matheagle's Avatar
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    Quote Originally Posted by jimmianlin View Post
    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
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