# Bernoulli variance

1. Aug 1, 2010

### Gekko

1. The problem statement, all variables and given/known data

Show how Var(Xi) depends on p writing it as a function $$\sigma$$^2(p)

3. The attempt at a solution

Var[Xi] = E[Xi^2] - E^2[Xi] = p-p^2 = p(1-p)

not sure where to go from here to get it in the form $$\sigma^2$$(p) ?

2. Aug 1, 2010

### HallsofIvy

Please clarify you question. In particular, what is "p"? The mean?

If I understand the rest, The standard deviation, $\sigma$ is defined as the square root of the variance. The variance is $\sigma^2$.

3. Aug 1, 2010

### Gekko

p in this case is the probability of success. Xi is a Bernoulli random variable.

This is a standard Bernoulli question but I just dont understand what the question is asking when it says "writing it as a function sigma^2(p)". Does that mean calculate the variance of the probability? Surely not. In which case it must just be p(1-p)?

4. Aug 1, 2010

think about common function notation: when you write a function of $$x$$ you use $$f(x)$$. Since the variance in the binomial setting is a function of $$p$$, the corresponding way to write it is $$\sigma^2(p)$$ - variance as a function of $$p$$. It looks awkward, but you're stuck with it.