IXL - Standard deviation of random variables (Precalculus practice)

The table below shows the probability distribution of a random variable

Y	P ( Y )
11	0.6
12	0.2
13	0.1
14	0.1

What is the standard deviation of

Round your answer to the nearest hundredth.

ref_doc_title.

Learn with an example

question

The table below shows the probability distribution of a random variable

Y	P ( Y )
0	0.4
1	0.1
2	0.3
3	0.2

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 )
0	0.4	0
1	0.1	0.1
2	0.3	0.6
3	0.2	0.6

(

)

0.1

0.6

1.3

So, the expected value of

is 1.3.

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 )
0	0.4	1.69	0.676
1	0.1	0.09	0.009
2	0.3	0.49	0.147
3	0.2	2.89	0.578

𝜎

0.676

0.009

0.147

0.578

1.41

Find the standard deviation of

To find

𝜎

the standard deviation of

take the square root of

𝜎

1.41

≈

1.19

Looking for more? Try this:

$Confetti$

Excellent!

Now entering the Challenge Zone—are you ready?

Questions
answeredQuestions

Time
elapsedTime

hr	min	sec
00	00	04

SmartScore
out of 100
IXL's SmartScore is a dynamic measure of progress towards mastery, rather than a percentage grade. It tracks your skill level as you tackle progressively more difficult questions. Consistently answer questions correctly to reach excellence (90), or conquer the Challenge Zone to achieve mastery (100)! Learn more

Teacher tools

Work it out

Not feeling ready yet? This can help:

DD.6Variance of random variables

Excellent! You got that right!

Jumping to level 1 of 1

Excellent!