Bernoulli Variance: Calculating Var[Xi] as a Function of p

[Gekko]

Homework Statement

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

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) ?

 

[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 $\sigma^2$.

 

[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 don't 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)?

 

[statdad]

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.

 

[Gekko]

I see. That makes sense. Thanks