# 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)