1. Apr 3, 2010 #1

   scottstapp

   

   1. The problem statement, all variables and given/known data
   
   Suppose we want to estimate a binomial proportion, p. We take a sample of size n and count X successes.
   
   Consider a Bernoulli random variable, Y that is 1 with probability p and 0 otherwise. Show that the mean and variance of Y are p and p(1-p), respectively.
   
   
   
   2. Relevant equations
   
   
   
   3. The attempt at a solution
   Not too sure what to do here. I know that the mean is calculated by [tex]\Sigma[/tex]xf(x) and variance is E(X-mean)²

    

   scottstapp, Apr 3, 2010
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3. Apr 3, 2010 #2

   rock.freak667

   

   Homework Helper

   Well write out your sample space
   
   
   y 0 1
   P(Y=y)
   
   
   For y=p, your probability is?
   
   and in any other case such as y=0, the probability is?
   
   Then you just use your definition E(Y)=∑_{all y} y P(Y=y)

    

   rock.freak667, Apr 3, 2010

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