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).

Answer 1

Answer with Step-by-step explanation:

We are given that

$\lambda=2$

a.Mean waiting time,$E(T)=\frac{1}{\lambda}$

$E(T)=\frac{1}{2}=0.5 s$

b.Median waiting time,$P(T$

$1-e^{-\lambda t_{md}}=0.5$

Where $P(T$

$e^{-\lambda t_{md}}=1-0.5=0.5$

$e^{-2t_{md}}=0.5$

$-2t_{md}=ln(0.5)$

$-2t_{md}=-0.693$

$t_{md}=\frac{0.693}{2}=0.3465 s$

c.P(T>2)=$1-P(T< 2)=1-(1-e^{-2\times 2})$

$P(T>2)=e^{-4}=0.018$

d.$P(T$