# Probability-Moments and Cumulants (ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)): Questions 1 - 1 of 1

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## Question number: 1

» Probability » Moments and Cumulants

Appeared in Year: 2013

Essay Question▾

### Describe in Detail

Compute the factorial moments µ _{ (r) } and the cumulants k _{r}, r = 1,2, …. . , of Poisson distribution with parameter m.

### Explanation

Let X follows Poisson distribution with parameter m. The density function is

The r ^{th} factorial moment of Poisson distribution is

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