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Ron P
Ron P
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I'm looking for a lower bound for the probability that an arbitrary convex combination of iid Bernoulli (p) random variables is at least p. My guess is p/2k (for some constant k; k must be at least e, as noted by Matt below), but I'm happy with any positive lower bound that depends only on p.

For example, if p is slightly above 1/2, and the convex combination is simply the average of two variables, then the probability is slightly above 1/4 which is approximately p/2.

I'm looking for a lower bound for the probability that an arbitrary convex combination of iid Bernoulli (p) random variables is at least p. My guess is p/2, but I'm happy with any positive lower bound that depends only on p.

For example, if p is slightly above 1/2, and the convex combination is simply the average of two variables, then the probability is slightly above 1/4.

I'm looking for a lower bound for the probability that an arbitrary convex combination of iid Bernoulli (p) random variables is at least p. My guess is p/k (for some constant k; k must be at least e, as noted by Matt below), but I'm happy with any positive lower bound that depends only on p.

For example, if p is slightly above 1/2, and the convex combination is simply the average of two variables, then the probability is slightly above 1/4 which is approximately p/2.

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Ron P
Ron P
  • 947
  • 6
  • 15

Convex combination iid Bernoulli random variables

I'm looking for a lower bound for the probability that an arbitrary convex combination of iid Bernoulli (p) random variables is at least p. My guess is p/2, but I'm happy with any positive lower bound that depends only on p.

For example, if p is slightly above 1/2, and the convex combination is simply the average of two variables, then the probability is slightly above 1/4.