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)