Home › MCQs › CSS Statistics › Question #1990
Back to Questions
CSS Statistics QUESTION #1990
Question 1
For the Poisson distribution with parameter \(\lambda\), which of the following statements is INCORRECT?
  • Mean = Variance = \(\lambda\)
  • The distribution is always positively skewed for finite \(\lambda\)
  • The mgf is \(M(t) = e^{\lambda(e^t - 1)}\)
  • As \(\lambda \to \infty\), the Poisson distribution approaches the t-distribution✔️
Correct Answer Explanation
The mean, variance, and mgf statements are all correct properties of the Poisson distribution. As \(\lambda \to \infty\), the Poisson distribution approaches the NORMAL distribution (not the t-distribution), by the Central Limit Theorem. This is what makes statement (D) incorrect.