# Quiz 1: Discrete Distributions

Test your knowledge of the material on discrete distributions in the
following quiz.

**What are the assumptions necessary for a variable to be
distributed as a binomial distribution?**

- The variable must be binary
- The variable must be discrete
- The variable must have a fixed number of trials
- All of the above

**How does the skewness of a binomial variable relate to its
parameters ***n* and *p*?

- Skewness = n p
- Skewness = n/p
- Skewness = p (1-p) / n
- Skewness = p^2 / n

**When would you use a negative binomial distribution over a
Poisson distribution?**

- When the number of trials is fixed
- When the variance exceeds the mean
- When there are negative counts in the data
- When the parameter p differs substantially from 0.5

**How does the mean and variance of a Poisson distribution
relate to its parameter λ?**

- Mean = λ, Variance = λ
- Mean = 1/λ, Variance = 1/λ^2
- Mean = 1/λ, Variance = λ
- Mean = λ, Variance = λ^2

**Which example is most likely to follow a log-series
distribution?**

- Number of accidents at a busy intersection
- Counts of occurrences of distinct words in the books written by Jane
Austin
- Number of births of males in Canadian families composed of 6
children
- Number of tosses of a coin required to get the first head.

- **Which of the following characterize the negative binomial
distribution and the geometric distribution?

- The negative binomial distribution models the number of failures
before a specified number of successes
- The geometric distribution models the number of failures before the
first success
- Both A and B
- Neither A nor B

**In what type of data might you use a negative binomial
distribution?**

- Count data
- Binary data
- Continuous data
- Both A and B

**What is the mean and variance of a variable distributed as a
geometric distribution?**

- Mean = λ, Variance = λ
- Mean = 1/λ, Variance = 1/λ^2
- Mean = 1/λ, Variance = λ
- Mean = λ, Variance = 1/λ^2

## Answers

1: d; 2: c; 3: b; 4: a; 5: b; 6: c; 7: b (bad question– DDAR defines
the geometric distribution in terms of the parameter *p*); 8:
d