# Worksheet: Variance of Discrete Random Variables

In this worksheet, we will practice calculating the variance of discrete random variables.

Q1:

Suppose and are independent, , and . Determine .

Q2:

Suppose and are independent, , and . Determine .

Q3:

Suppose and are independent, , and . Determine .

Q4:

Suppose that , are two independent variables. Given that , , and , find .

• A3
• B6
• C9
• D21
• E30

Q5:

If and are two independent random variables, is ?

• ANo
• BYes

Is ?

• ANo
• BYes

Q6:

Suppose and are two independent variables such that , where is a constant. Determine .

Q7:

Suppose and are two independent variables such that and . Determine .

Q8:

Suppose and are two independent variables such that and . Determine .

Q9:

Suppose that , are two independent variables. Given that , , and , find .

Q10:

Suppose that and are two independent variables.

If and , determine .

If , find .

If , find .

Find .

Q11:

Suppose and are two independent variables such that . If is a constant, determine .

Q12:

Let and be two independent random Variables.

Suppose that we know and .

Find and .

• A and
• B and
• C and
• D and
• E and

Q13:

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

Q14:

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

Q15:

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

Q16:

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.

Q17:

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.

Q18:

Given that , find

Q19:

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.

Q20:

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

Q21:

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.

Q22:

Given that , find

Q23:

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.

Q24:

An experiment that produces the discrete random variable has the probability distribution shown.

 𝑥 𝑝(𝑥) 2 3 4 5 0.1 0.3 0.2 0.4

Calculate .

Calculate .

The variance of can be calculated using the formula . Calculate to 2 decimal places.

Q25:

The probability mass functions for and are shown. Calculate the variance of and then the variance of . If necessary, round your answer to the nearest hundredth.

 𝑋 𝑃(𝑋) 8 7 2 0.17 0.33 0.5
 𝑌 𝑃(𝑌) 9 5 4 7 0.3 0.4 0.24 0.06
• Avariance of is 2.69, variance of is 2.03
• Bvariance of is 4.11, variance of is 7.24
• Cvariance of is 2.03, variance of is 2.69
• Dvariance of is 7.24, variance of is 4.11
• Evariance of is 2.69, variance of is 4.11