How do you compute the variance of the probability distribution in the table provided?
Outcome | Probability
50 | 0.5
51 | 0.2
52 | 0.1
53 | 0.2?
Outcome | Probability
50 | 0.5
51 | 0.2
52 | 0.1
53 | 0.2?
1 Answer
Var(X) = 1.4
Explanation:
Let
First we quickly check that
The, we calculate
So then the Expectation is calculated using:
E(X) = sum xP(x)
" " = 25+10.2+5.2+10.6
" " = 51
Next prior to calculating the Variance we calculate E(X^2):
E(X^2) = sum x^2P(x)
" " = 1250+520.2+270.4+561.8
" " = 2602.4
Then we can calculate the variance:
Var(X) = E(X^2) - E^2(X)
" " = 2602.4- (51)^2
" " = 2602.4- 2601
" " = 1.4
We can also calculate the Standard Deviation (if required); as
sigma^2 = Var(X) => sigma = 1.18 (3sf)