Problem 8E

A radioactive mass emits particles according to a Poisson process at a mean rate of 2 per second.

Let T be the waiting time, in seconds, between Emissions.

a. What is the mean waiting time?

b. What is the median waiting time?

c. Find P(T > 2).

d. Find P(T<0.1).

e. Find P(0.3<T<1.5).

f. If 3 seconds have elapsed with no emission, what is the probability that there will be an emission within the next second?

Solution

Step 1 of 7

Here given radioactive mass emits the particles according to the poisson distribution with mean

The pmf of exponential distribution is

The CDF of exponential distribution is

Let T be the waiting time between emissions

Here T follows exponential distribution with parameter