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?

1 Answer
Feb 27, 2017

Var(X) = 1.4

Explanation:

Let X be the Random Variable that represents a possible outcome:

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First we quickly check that sumP(x) = 1 which is indeed the case.

The, we calculate x^2, xP(x), and x^2P(x):

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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)