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Unknown to public health officials a person with a highly

Unknown to public health officials, a person with a highly contagious disease enters the population. During each period he either infects a new person which occurs with probability p, or his symptoms appear and he is discovered by public health officials, which occurs with probability 1-p. Compute the probability distribution of the number of infected but undiscovered people in the population at the time of first discovery of a carrier. Assume each infective behaves like the first.

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