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[3] The emission of particles from a radioactive mass constitutes a Poisson process with emission
rate 2.5 particles per second. (a) Find the probability that at least two particles are emitted in the
first two seconds the mass is observed. (b) If no particle is emitted in the first second, find the
probability that a particle is emitted in the next second. (c) Find the expected time until the
emission of the first particle.

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  • 1. [3] The emission of particles from a radioactive mass constitutes a Poisson process with emission rate 2.5 particles per second. (a) Find the probability that at least two particles are emitted in the first two seconds the mass is observed. (b) If no particle is emitted in the first second, find the probability that a particle is emitted in the next second. (c) Find the expected time until the emission of the first particle.