Pulses arrive at a Geiger counter in accordance with a Poisson process at a rate of three

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Pulses arrive at a Geiger counter in accordance with a Poisson process at a rate of three arrivals per minute. Each particle arriving at the counter has a probability of being recorded. Let X(r) denote the number of pulses recorded by time minutes.

(a) P(X(r) = 0) = ?

(b) E[X(t)] = ?

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