Mathematics · Probability Distributions
Suppose X ~ Geometric(1/2) taking values in {1, 2, 3, ...} and conditional on X, the variable Y has a Poisson(X) distribution. Similarly, suppose U ~ Poisson(1) and conditional on U, the variable V has a Geometric(1/(U + 1)) distribution taking values in {1, 2, 3, ...}. Which of the following relationships between variances is correct?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1E[Y] < E[V]
- 2E[Y] > E[V]
- 3Var[Y] > Var[V]✓
- 4Var[Y] < Var[V]
Correct answer
Var[Y] > Var[V]
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