Question

How to apply these formulas for Mean and Variance in Finance?

With examples and what the letters mean, thank you

Mean

E(?? ) = 1 ? ∑??,? ? ?=1

Variance

VAR(?? ) = 1 ? − 1 ∑[??,? − ?(?? )] 2 ? ?=1 ,

Answer 1

Mean or Expected Value: μ

When we know the probability p of every value x we can calculate the Expected Value (Mean) of X:

μ = Σxp

Note: Σ is Sigma Notation, and means to sum up.

To calculate the Expected Value:

• multiply each value by its probability
• sum them up

Example : Tossing a die we have equal opportunity to get no. 1-6

x	1	2	3	4	5	6
p	0.1	0.1	0.1	0.1	0.1	0.1
xp	0.1	0.2	0.3	0.4	0.5	0.6

μ = Σxp = 0.1+0.2+0.3+0.4+0.5+0.6= 2.1

The expected value / mean is 2.1

The variance (σ²) is a measure of how far each value in the data set is from the mean.

Var(X) = Σx²p − μ²

To calculate the Variance:

• square each value and multiply by its probability
• sum them up and we get Σx²p
• then subtract the square of the Expected Value μ²

Example continued:

x	1	2	3	4	5	6
p	0.1	0.1	0.1	0.1	0.1	0.1
x2p	0.1	0.4	0.9	1.6	2.5	3.6

Σx²p = 0.1+0.4+0.9+1.6+2.5+3.6 = 9.1

Var(X) = Σx²p − μ² = 9.1 - 2.1² = 4.69

The variance is 4.69