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 .
- 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.
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
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 | |
- 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.