# Worksheet: Standard Deviation and Variance of Discrete Random Variables

In this worksheet, we will practice calculating the variance and standard deviation of a probability distribution.

Q1:

The function in the given table is a probability function of a discrete random variable . Find the standard deviation of . Give your answer to two decimal places.

 𝑥 𝑓(𝑥) −5 −4 −3 −1 13 18 14 724

Q2:

The function in the given table is a probability function of a discrete random variable . Find the standard deviation of . Give your answer to two decimal places.

 𝑥 𝑓(𝑥) 4 6 10 819 819 319

Q3:

The function in the given table is a probability function of a discrete random variable . Given that the expected value of is 6.5, find the standard deviation of . Give your answer to two decimal places.

 𝑥 𝑓(𝑥) 3 𝐴 6 8 0.2 0.1 0.1 0.6

Q4:

The function in the given table is a probability function of a discrete random variable . Find the variance of . If necessary, give your answer to two decimal places.

 𝑥 𝑓(𝑥) 3 5 7 8 2𝐴 5𝐴 5𝐴 𝐴

Q5:

The function in the given table is a probability function of a discrete random variable . Given that the expected value of is , find the variance of . Give your answer to two decimal places.

 𝑥 𝑓(𝑥) 1 2 𝐵 7 10𝑎 4𝑎 12 6𝑎

Q6:

Can the function in the given table be a probability distribution function?

 𝑥 𝑓(𝑥) 0 1 4 5 0.17 0.43 0.69 0.36
• Ano
• Byes

Q7:

A die is rolled two successive times. If the random variable denotes the sum of numbers appearing on the upper face after each roll, find the range of .

• AThe range of the random variable
• BThe range of the random variable
• CThe range of the random variable
• DThe range of the random variable
• EThe range of the random variable

Q8:

Let denote a discrete random variable which can take the values . Given that has probability distribution function , find the standard deviation of . Give your answer to 2 decimal places.

Q9:

Let denote a discrete random variable which can take the values . Given that has probability distribution function , find the variance of .

• A0
• B
• C
• D

Q10:

Let denote a discrete random variable which can take the values 2, 4, and 5. Given that has probability distribution function , find the variance of . Give your answer to two decimal places.

Q11:

Given that , find

Q12:

Let denote a discrete random variable which can take the values and 5. Given that , , and , find the value of .

Q13:

Let denote a discrete random variable which can take the values 3, 5, and 6. Which of the following functions could represent the probability function of ?

• A
• B
• C
• D

Q14:

Which of the following is not a discrete random variable?

• AThe number of cars in a family.
• BThe number of children in a family.
• CThe average height of children in a family.
• DThe number of children taller than 4 ft in a family.

Q15:

Let denote a discrete random variable which can take the values 2, 6, 7, and 8. Given that and , find . Give your answer as a fraction.

• A
• B
• C
• D

Q16:

Let denote a discrete random variable which can take the values . Given that has probability distribution function , find the value of .

• A
• B
• C
• D

Q17:

The function in the given table is a probability function of a discrete random variable . Find the value of .

 𝑥 𝑓(𝑥) 0 1 2 3 3𝑎 8𝑎 4𝑎 8𝑎
• A1
• B
• C
• D

Q18:

Let denote a discrete random variable which can take the values and 4. Given that ,, and , find the value of .

Q19:

Let denote a discrete random variable which can take the values 0, 1, 3, and 4. Given that , , , and , find the value of .

• A
• B
• C
• D

Q20:

Let denote a discrete random variable which can take the values 1, 2, 3, 4, 5, and 6. Given that has probability distribution function , find the value of .

• A
• B
• C
• D

Q21:

Let denote a discrete random variable which can take the values . Given that has probability distribution function , find the variance of . Give your answer to two decimal places.

Q22:

Let denote a discrete random variable which can take the values 3, 4, and 5. Given that , find the variance of . If necessary, give your answer to two decimal places.

Q23:

Let denote a discrete random variable which can take the values 2, 3, 5, and 8. Given that , , , and , find the variance of . Give your answer to two decimal places.

Q24:

Let denote a discrete random variable which can take the values . Given that has probability distribution function , find the variance of .

• A8
• B
• C
• D31

Q25:

Let denote a discrete random variable which can take the values 1, 2, 7, and 8. Given that , , and , find the variance of . Give your answer to two decimal places.