IXL - Variance of random variables (Algebra 2 practice)

The table below shows the probability distribution of a random variable

Z	P ( Z )
2	0.6
3	0.1
4	0
5	0.3

What is the variance of

Write your answer as a decimal. Do not round.

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Learn with an example

question

The table below shows the probability distribution of a random variable

Z	P ( Z )
8	0.2
9	0.2
10	0.6

What is the variance of

Write your answer as a decimal. Do not round.

key idea

A random variable is a function that assigns a numerical value to each outcome in a sample space. Note that though random variables are functions, they are usually denoted by capital letters like

is a random variable,

(

)

(

)

is the probability that

takes the value

The function that maps

(

)

is the probability distribution of

A probability distribution is frequently represented as an equation, table or graph.

The expected value or mean

(

)

of a random variable

is the sum of the terms

(

)

for each value

that

can take. It is also called the expected value or mean of the probability distribution of

and is sometimes written

𝜇

The

variance,

𝜎

of a random variable

is the sum of the terms

[

–

(

)

]

(

)

for each value

that

can take. It is also called the variance of the probability distribution of

solution

Find the expected value of

To find

(

the expected value of

find

(

)

for each value

that

can take. Then, sum these terms.

Z	P ( Z )	Z P ( Z )
8	0.2	1.6
9	0.2	1.8
10	0.6	6

(

)

1.6

1.8

9.4

So, the expected value of

is 9.4.

Find the variance of

To find

𝜎

the variance of

find

(

–

(

)

(

)

for each value

that

can take. Then, sum these terms.

Z	P ( Z )	( Z – E ( Z ) ) 2	( Z – E ( Z ) ) 2 P ( Z )
8	0.2	1.96	0.392
9	0.2	0.16	0.032
10	0.6	0.36	0.216

𝜎

0.392

0.032

0.216

0.64

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PP.5Expected values of random variables

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