X ~ Bin(3,p) show that E(X) = 3p

[adamwitt]

X ~ Bin(3,p) ... show that E(X) = 3p

Homework Statement

Given X ~ Bin(3,p) ... show that E(X) = 3p

Homework Equations

Unsure. Possibly...

P(k) = [n! / (k!*(n-k)!)] * (p^k) * (1-p)^(n-k)

E(X) = Expected value of X = Sum[(Probability of X)*(X)]

The Attempt at a Solution

I have a whole heap of scribble on my paper but none of it is worth typing up because I have no idea how to show this, although it seems like something incredibly simple. I think I am missing something, like a property of Binary distributions or something that could allow me to work out the answer...arghhh

 

[Gregg]

Yeah that is the right definition for expectation

 

[adamwitt]

Well I did that and I end up getting E(X) = 6p ?

E(X) = (0)p + (1)p + (2)p + (3)p = 6p

I know I am doing something dumb here, but i can't work out what!

 

[Gregg]

For the binomial!

$$P(X=x)\ne p$$

What's the $$P(X=x) ?$$