A radioactive mass emits particles according to a Poisson pr

A radioactive mass emits particles according to a Poisson process at a mean rate of 12 particles per minute. At some point, a clock is started. Round probability to four decimal places.

1.What is the probability that more than 7 seconds will elapse before the next emission?

2. What is the mean waiting time until the next particle is emitted?

Solution

1) If we consider poisson parameter for particles per minute for Y

then for seconds we take exponential distribution with parameter 1/12

Hence for 10 second parameter = 5 seconds.

1) P(X>10) = P(Y<6) = 0.0203

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2) Mean waiting time = 1/12 = 5 seconds.