IXL - Standard deviation of random variables (Algebra 2 practice)

The table below shows the probability distribution of a random variable

X	P ( X )
18	0.4
19	0.2
20	0.4

What is the standard deviation of

Round your answer to the nearest hundredth.

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Learn with an example

question

The table below shows the probability distribution of a random variable

Y	P ( Y )
5	0.3
6	0.2
7	0
8	0.5

What is the standard deviation of

Round your answer to the nearest hundredth.

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

The square root of the variance,

𝜎

is called the standard deviation of a random variable

It is also called the standard deviation 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.

Y	P ( Y )	Y P ( Y )
5	0.3	1.5
6	0.2	1.2
7	0	0
8	0.5	4

(

)

1.5

1.2

6.7

So, the expected value of

is 6.7.

Find the variance of

To find

𝜎

the variance of

find

(

–

(

)

(

)

for each value

that

can take. Then, sum these terms.

Y	P ( Y )	( Y – E ( Y ) ) 2	( Y – E ( Y ) ) 2 P ( Y )
5	0.3	2.89	0.867
6	0.2	0.49	0.098
7	0	0.09	0
8	0.5	1.69	0.845

𝜎

0.867

0.098

0.845

1.81

Find the standard deviation of

To find

𝜎

the standard deviation of

take the square root of

𝜎

1.81

≈

1.35

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