# Worksheet: Variance of Discrete Random Variables

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

**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.

3 | 5 | 7 | 8 | |

**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.

1 | 2 | 7 | ||

**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.

**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.

**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.

8 | 7 | 2 | |

0.17 | 0.33 | 0.5 |

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