Random variable, expected value,Variance

1. Oct 16, 2011

philipSun

Hi.
I choose randomly a one word, and I decided to choose a word blue. Let random variable x be a length of the word blue. What is expected value and variance of a word blue?

So, random variable x = 4.

E(X) = Ʃ xi fX(xi)
i:xi∈S

x1 + x2 + x3 + x4 = 10.

expected value = 10.

Variance is

Var(X) = E[X − E(X)]^2

Var(X) = E[10 − E(4)]^2 = 6^2 = 36

Variance = 36

2. Oct 17, 2011

philipSun

I do a little improvement.

E(X) = Ʃ xi f(x)p(x)
i:p(x)∈S

x1 + x2 + x3 + x4 = 10.

expected value = 10. Is this correct?

Variance is

Var(X) = E[X − E(X)]^2

Var(X) = E[10 − E(4)]^2 = 6^2 = 36

Variance = 36. Is this correct?

3. Oct 17, 2011

mathman

The problem as described has a mean of 4 (blue has 4 letters) and a variance of 0 (blue has 4 letters - no variation).

4. Oct 18, 2011

philipSun

Can you formalize those solutions?

I don't understand.
Do you mean that expected value is 4 ? Mean = expected value?

And because blue has 4 letters - no variation. so variance is

Var(X) = E[4 − E(4)]^2 = 0 ??

5. Oct 18, 2011

mathman

Mean = expected value (almost by definition - since mean may be defined as sample mean or true mean - the expected value).

Var(X) = 0, as you described.