Answer with Step-by-step explanation:
We are given that
[tex]\lambda=2[/tex]
a.Mean waiting time,[tex]E(T)=\frac{1}{\lambda}[/tex]
[tex]E(T)=\frac{1}{2}=0.5 s[/tex]
b.Median waiting time,[tex]P(T<t_{md})=E(T)=0.5[/tex]
[tex]1-e^{-\lambda t_{md}}=0.5[/tex]
Where [tex]P(T<t)=1-e^{-\lambda t}[/tex]
[tex]e^{-\lambda t_{md}}=1-0.5=0.5[/tex]
[tex]e^{-2t_{md}}=0.5[/tex]
[tex]-2t_{md}=ln(0.5)[/tex]
[tex]-2t_{md}=-0.693[/tex]
[tex]t_{md}=\frac{0.693}{2}=0.3465 s[/tex]
c.P(T>2)=[tex]1-P(T< 2)=1-(1-e^{-2\times 2})[/tex]
[tex]P(T>2)=e^{-4}=0.018[/tex]
d.[tex]P(T<0.1)=1-e^{-2\times 0.1}=1-e^{-0.2}=0.181[/tex]
