Free Practice Quiz Question List

5 Expectation and Variability Online Quiz Questions

Use this free practice quiz with 20 questions to review 5 Expectation and Variability, test your knowledge, and prepare for your next test or exam.

20 questions

Choose one

1 point

Which statement correctly describes the expectation of a random variable?

A
The expected value must be one of the possible outcomes.
B
The expected value can lie between possible outcomes and need not itself be attainable.
C
The expected value is always the most probable outcome.
D
The expected value is the same as the variance.

Choose one

1 point

If $E[X]=4$ , what is $E[2X+3]$ ?

A
11
B
8
C
7
D
5

Choose one

1 point

Two independent measurements have standard deviations 3 and 4. What is the standard deviation of their sum?

A
7
B
25
C
5
D
12

Choose all

1 point

Select all statements that are correct about sums of random variables.

A
The expectation of a sum equals the sum of the expectations without requiring independence.
B
If independent variables have the same variance, their sum has that same variance.
C
Independence makes the covariance terms in the variance of a sum equal to zero.
D
The standard deviations of independent variables always add directly.

Choose all

1 point

Select all statements that correctly describe variance and standard deviation.

A
Variance is measured in the same units as the variable.
B
Adding a constant does not change variance.
C
Standard deviation is measured in squared units.
D
Multiplying a variable by $a$ multiplies its variance by $a^2$ .

True or false

1 point

True or false: The variance can be computed as $E[X^2]-\bigl(E[X]\bigr)^2$ .

A
True
B
False

True or false

1 point

If two random variables have covariance zero, they must be independent.

A
True
B
False

Written response

1 point

For a fair six-sided die, what is the expected value $E[X]$ ? Enter the value as a decimal.

Fill in the blank

1 point

If two random variables are independent and their expectations exist, their is zero.

Fill in the blank

1 point

If a measurement is recorded in meters, its variance is measured in .

Open ended

1 point

Explain how the expectation and standard deviation of a sum of $n$ random variables behave. Include the role of dependence, and state the results when the variables are mutually independent and identically distributed.

Choose one

1 point

Suppose $\operatorname{Var}(X)=9$ , $\operatorname{Var}(Y)=16$ , and $\operatorname{Cov}(X,Y)=2$ . What is $\operatorname{Var}(X+Y)$ ?

A
21
B
25
C
29
D
41

Choose one

1 point

A fair six-sided die is rolled repeatedly. What is the expected value of the outcome on one roll?

A
3
B
3.5
C
4
D
6

True or false

1 point

True or false: The equality $E[X+Y]=E[X]+E[Y]$ requires $X$ and $Y$ to be independent.

A
True
B
False

Choose one

1 point

If $\operatorname{Var}(X)=v$ , which expression gives $\operatorname{Var}(2X+3)$ ?

A
$\operatorname{Var}(X)$
B
$2\operatorname{Var}(X)$
C
$4\operatorname{Var}(X)$
D
$5\operatorname{Var}(X)$

Written response

1 point

Two variables tend to be above their means at the same time and below their means at the same time. What is the sign of their covariance?

Choose one

1 point

A random variable measures length in meters. In what units is its variance measured?

A
Meters
B
Meters per second
C
Dimensionless units
D
Square meters

Written response

1 point

Two independent measurements have standard deviations 3 and 4. What is the variance of their sum?

Choose one

1 point

Which statement correctly describes the relationship between independence and covariance?

A
Zero covariance does not generally imply independence.
B
Zero covariance always implies independence.
C
Independence requires covariance to be positive.
D
Covariance can be zero only when both variables are constant.

Written response

1 point

A sample contains the observations $1$ , $2$ , and $3$ . What is the sample variance $s^2$ , using the denominator $n-1$ ? Enter the value as a decimal.