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?
Step 1 of 7</p>
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
Step 2 of 7</p>
a) We have to find the mean of the waiting time
The mean of exponential distribution is
Hence the mean of the waiting time is 0.5 seconds
Step 3 of 7</p>
b) We have to find median waiting time
Let a be the median
Hence the median waiting time is 0.3466
Step 4 of 7</p>
c) we have to find P(T>2)
Hence P(T>2) is 0.0183