Not sure if this is allowed but you can aim at a rock or similar say 10m away from the target (4km from you) to get the bias (and distribution if multiple shots are allowed). Also if the distribution is not totally normal, but has smaller than normal tails then you could aim off target with multiple shots to get the highest chance of hitting the target. For example if the child is head height then aim for the targets feet, or even aim 1m below the target feet expecting 1⁄100 shots will actually hit the targets legs, but only <1/1000 say will hit the child. That is assuming an unrealistic amount of shots of course. If you have say 10 shots, then some combined strategy where you start aiming a lot off target to get the bias and a crude estimate of the distribution, then steadily aiming closer could be optimal.
Not sure if this is allowed but you can aim at a rock or similar say 10m away from the target (4km from you) to get the bias (and distribution if multiple shots are allowed). Also if the distribution is not totally normal, but has smaller than normal tails then you could aim off target with multiple shots to get the highest chance of hitting the target. For example if the child is head height then aim for the targets feet, or even aim 1m below the target feet expecting 1⁄100 shots will actually hit the targets legs, but only <1/1000 say will hit the child. That is assuming an unrealistic amount of shots of course. If you have say 10 shots, then some combined strategy where you start aiming a lot off target to get the bias and a crude estimate of the distribution, then steadily aiming closer could be optimal.