# 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.

**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.

3 | 5 | 7 | 8 | |

**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.

1 | 2 | 7 | ||

**Q6: **

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

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 .

- A The range of the random variable
- B The range of the random variable
- C The range of the random variable
- D The range of the random variable
- E The 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 .

- A
- B
- C0
- 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 . If necessary, give your answer to two decimal places.

**Q11: **

Given that , find

**Q12: **

Let denote a discrete random variable which can take the values . 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 taller than 4 ft in a family.
- CThe number of children in a family.
- DThe average height of children 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 .

0 | 1 | 2 | 3 | |

- A
- B
- C1
- D

**Q18: **

Let denote a discrete random variable which can take the values . 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 .

- A31
- B8
- C
- D

**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.