Mathematics · Probability and Statistics
Suppose X 1 , X 2 , ..., X n are i.i.d. random variables with characteristic function φ(t; θ) = E[e itX 1 ] where θ ∈ &re; k is the parameter of the distribution. Let Z = X 1 + X 2 + ... + X n . Then for which of the following distributions of X 1 would the characteristic function of Z be of the form φ(t; α) for some α ∈ &re; k ?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1Discrete Uniform
- 2Hypergeometric
- 3Geometric
- 4Negative Binomial✓
Correct answer
Negative Binomial
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