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

=0.5

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

Then

=0.5

=0.5

0.3466

Hence the median waiting time is 0.3466

Step 4 of 7</p>

c) we have to find P(T>2)

P(T>2)=

=1-()

=

=0.0183

Hence P(T>2) is 0.0183