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Bernoulli random variable problem

  • Thread starter scottstapp
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  • #1
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Homework Statement



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.



Homework Equations





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
 

Answers and Replies

  • #2
rock.freak667
Homework Helper
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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
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)
 

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