IXL - Expected values of random variables (Algebra 2 practice)

The table below shows the probability distribution of a random variable

X	P ( X )
10	0.1
11	0.7
12	0.2

What is the expected value of

Write your answer as a decimal.

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Learn with an example

question

The table below shows the probability distribution of a random variable

Z	P ( Z )
5	0
6	0.1
7	0.6
8	0.3

What is the expected value of

Write your answer as a decimal.

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

solution

To find

(

the expected value of

find

(

)

for each value

that

can take. Then, sum these terms.

Z	P ( Z )	Z P ( Z )
5	0	0
6	0.1	0.6
7	0.6	4.2
8	0.3	2.4

(

)

0.6

4.2

2.4

7.2

So, the expected value of

is 7.2.

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Work it out

Not feeling ready yet? These can help:

PP.3Write a discrete probability distribution

D.1Add and subtract decimals

D.3Multiply decimals

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