IXL - Expected values of random variables (Precalculus practice)

The table below shows the probability distribution of a random variable

X	P ( X )
11	0.2
12	0.4
13	0.1
14	0.3

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

Y	P ( Y )
4	0.1
5	0.1
6	0.8

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.

Y	P ( Y )	Y P ( Y )
4	0.1	0.4
5	0.1	0.5
6	0.8	4.8

(

)

0.4

0.5

4.8

5.7

So, the expected value of

is 5.7.

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