EX 3.41 pulse

• Pulses arrive at a counter:
  • Average rate: 6 pulses per minute
  • Parameter: $\alpha =6$
• Calculation of probability:
  • Time interval: 0.5 minutes
  • Number of pulses in this interval:
    • Follows a Poisson distribution
    • Parameter: $\alpha t=6\cdot 0.5=3$
  • 0.5 minutes used because $\alpha$ is expressed as a rate per minute
• Notation:
  • Let $X$ denote number of pulses received in the 30-second interval
• We have

$$\begin{array}{rl}P(1\le X)& =1-P(X=0)\\ & =1-\frac{e^{-3}(3{)}^0}{0!}\\ & =0.950\end{array}$$