i. The random variable for a Poisson probability distribution is discrete. ii. The Poisson probability distribution is always negatively skewed.
iii. The Poisson probability distribution has the same four characteristics as the binomial, but in addition, the probability of a success ($\pi$) is small and the number of trials (n) is relatively large.
A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question

Quizplus · Accepted Answer

- The random variable for a Poisson distribution is indeed discrete, as it counts occurrences in a fixed interval or space.- The Poisson distribution is not always negatively skewed; its skewness depends on the value of λ (the average rate of occurrence). It approaches symmetry as λ increases.- The statement about the Poisson distribution having similar characteristics to the binomial distribution, with the addition of a small success probability and a large number of trials, is a simplified way of differentiating between the conditions under which each distribution is typically applied. The Poisson distribution is often used as an approximation to the binomial distribution under these conditions.

I the Random Variable for a Poisson Probability Distribution Is π\piπ

I the Random Variable for a Poisson Probability Distribution Is $\pi$