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user44143
user44143

We can attack the baby problem directly, as Jairo Bochi and I did jointly in the comments.

For instance, the distribution which is a mixture of:

  • $3/5$ of a Bernoulli distribution with $p=1/2$
  • $2/5$ of a Beta distribution with $\alpha=\beta=4$

yields an integralexpectation equal to $503582/8204625$, or approximately $.0614$. This mixture of a discrete and a continuous distribution seems to be almost optimal.

We can attack the baby problem directly, as Jairo Bochi and I did jointly in the comments.

For instance, the distribution which is a mixture of:

  • $3/5$ of a Bernoulli distribution with $p=1/2$
  • $2/5$ of a Beta distribution with $\alpha=\beta=4$

yields an integral equal to $503582/8204625$, or approximately $.0614$. This mixture of a discrete and a continuous distribution seems to be almost optimal.

We can attack the baby problem directly, as Jairo Bochi and I did jointly in the comments.

For instance, the distribution which is a mixture of:

  • $3/5$ of a Bernoulli distribution with $p=1/2$
  • $2/5$ of a Beta distribution with $\alpha=\beta=4$

yields an expectation equal to $503582/8204625$, or approximately $.0614$. This mixture of a discrete and a continuous distribution seems to be almost optimal.

Source Link
user44143
user44143

We can attack the baby problem directly, as Jairo Bochi and I did jointly in the comments.

For instance, the distribution which is a mixture of:

  • $3/5$ of a Bernoulli distribution with $p=1/2$
  • $2/5$ of a Beta distribution with $\alpha=\beta=4$

yields an integral equal to $503582/8204625$, or approximately $.0614$. This mixture of a discrete and a continuous distribution seems to be almost optimal.