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Worksheet: Calculating Standard Deviation and Variance of Discrete Random Variables
Q8:
Given that , find
Q9:
Let denote a discrete random variable which can take the values . Given that , , and , find the value of .
Q10:
Let denote a discrete random variable which can take the values 3, 5, and 6. Which of the following functions could represent the probability distribution function of ?
- A
- B
- C
- D
Q11:
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
Q12:
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.
Q13:
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 | ||
Q14:
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
Q15:
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
Q16:
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
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 has probability distribution function , find the standard deviation of . Give your answer to 2 decimal places.
Q19:
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.
Q20:
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.
Q21:
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
Q22:
Let denote a discrete random variable which can take the values . Given that has probability distribution function , find the variance of .
- A
- B
- C
- D
Q23:
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.
Q24:
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 | |
Q25:
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.
| 1 | 3 | 5 | 7 | |