Poisson Distribution - why are these different?

[spitz]

Homework Statement

X(t) is a Poisson process with \lambda=0.2 events per second. What is the probability of zero events in 45 seconds?

2. The attempt at a solution

\frac{45}{0.2}=225 (0.2 second intervals)

so P[X=0] in 225 consecutive intervals is:

\left(e^{-0.2}\right)^{225} = 2.86 \times 10^{-20}

or

\lambda = (45)(0.2)=9 events per 45 seconds gives:

e^{-9} = 1.23 \times 10^{-4}

Both are approx. zero, but they are way different. How come?

 

[Ray Vickson]

Homework Statement

X(t) is a Poisson process with \lambda=0.2 events per second. What is the probability of zero events in 45 seconds?

2. The attempt at a solution

\frac{45}{0.2}=225 (0.2 second intervals)

so P[X=0] in 225 consecutive intervals is:

\left(e^{-0.2}\right)^{225} = 2.86 \times 10^{-20}

or

\lambda = (45)(0.2)=9 events per 45 seconds gives:

e^{-9} = 1.23 \times 10^{-4}

Both are approx. zero, but they are way different. How come?

The 0.2 is---as you stated originally--- the number of events per second; there is no 0.2 sec anywhere in the problem! In other words, 0.2/sec = (1/5)/sec = 1 per 5 sec. This is a good illustration of the old advice: always check your units (sec ≠ per sec).

RGV