Question: Consider a r.v. taking values x 1 ,x 2 , ...with probabilities p 1 , p 2 , ... , respectively. Let the x i

Consider a r.v. taking values x₁,x₂, ...with probabilities p₁, p₂, ... , respectively. Let the x_i’s be equally spaced, that is, x_i+1 −x_i equals the same number for all i. Assume that for a particular i, we replaced probabilities p_i−1, p_i, p_i+1 by probabilities p_i−1+Δ, p_i−2Δ, p_i+1+Δ where a positive Δ ≤ pi/2. Has the new distribution become worse or better in the EUM-risk-aversion case? Justify the answer.

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