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
2. 
   Phys.org - latest science and technology news stories on Phys.org

   • • Detecting metabolites at close range
   • • Research team uncovers lost images from the 19th century
   • • How community structure affects the resilience of a network
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

• Log in with Facebook
• Log in with Twitter

Your name or email address:

Do you already have an account?

• No, create an account now.
• Yes, my password is:
• Forgot your password?

Stay logged in