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A radioactive mass emits particles according to a Poisson
Chapter 4, Problem 8E(choose chapter or problem)
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?
Questions & Answers
QUESTION:
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?
ANSWER:Step 1 of 7
Here given radioactive mass emits the particles according to the poisson distribution with mean \(\lambda=2\)
The pmf of exponential distribution is \(f(x)=\lambda e^{-\lambda x}\)
The CDF of exponential distribution is \(F(x)=1-e^{-\lambda x}\)
Let T be the waiting time between emissions
Here T follows exponential distribution with parameter \(\lambda=2\)