Bernoulli random variable problem

[scottstapp]

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 $$\Sigma$$xf(x) and variance is E(X-mean)²

 

[rock.freak667]

The Attempt at a Solution

Not too sure what to do here. I know that the mean is calculated by $$\Sigma$$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)