Let X= \sum_{i=1}^{N} X_i, where X_i \sim Bernoulli(p_i). Let Y= \sum_{i=1}^N Y_i, where Y_i \sim Bernoulli(p_i+ \delta) for some 0 \leq \delta \leq 1- \max_i p_i.
Can we prove P(X \leq k) \geq P(Y \leq k), \forall k \in {0, \dots, N}?
Comparing Cdf of Poisson Binomial distribution for different parameters
Rakshith
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