Quiz 1: Discrete Distributions

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

  1. What are the assumptions necessary for a variable to be distributed as a binomial distribution?
  1. The variable must be binary
  2. The variable must be discrete
  3. The variable must have a fixed number of trials
  4. All of the above
  1. How does the skewness of a binomial variable relate to its parameters n and p?
  1. Skewness = n p
  2. Skewness = n/p
  3. Skewness = p (1-p) / n
  4. Skewness = p^2 / n
  1. When would you use a negative binomial distribution over a Poisson distribution?
  1. When the number of trials is fixed
  2. When the variance exceeds the mean
  3. When there are negative counts in the data
  4. When the parameter p differs substantially from 0.5
  1. How does the mean and variance of a Poisson distribution relate to its parameter λ?
  1. Mean = λ, Variance = λ
  2. Mean = 1/λ, Variance = 1/λ^2
  3. Mean = 1/λ, Variance = λ
  4. Mean = λ, Variance = λ^2
  1. Which example is most likely to follow a log-series distribution?
  1. Number of accidents at a busy intersection
  2. Counts of occurrences of distinct words in the books written by Jane Austin
  3. Number of births of males in Canadian families composed of 6 children
  4. Number of tosses of a coin required to get the first head.
  1. **Which of the following characterize the negative binomial distribution and the geometric distribution?
  1. The negative binomial distribution models the number of failures before a specified number of successes
  2. The geometric distribution models the number of failures before the first success
  3. Both A and B
  4. Neither A nor B
  1. In what type of data might you use a negative binomial distribution?
  1. Count data
  2. Binary data
  3. Continuous data
  4. Both A and B
  1. What is the mean and variance of a variable distributed as a geometric distribution?
  1. Mean = λ, Variance = λ
  2. Mean = 1/λ, Variance = 1/λ^2
  3. Mean = 1/λ, Variance = λ
  4. 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