In a town 10 accidents take place in the span of 50 days. Assuming that the number of accidents follows Poisson distribution, find the probability that there will be 3 or more accidents on a day. [ Given that \(e^{-0.2}=0.8187\) ]Solution : Here \(m=…

Q.6 (C) (ii) In a town 10 accidents take place in the span of 50 days. Assuming that the number of accidents follows Poisson distribution, find the probability that there will be 3 or more accidents on a day. [ Given that \(e^{-0.2}=0.8187\) ]

Solution : Here \(m=\square\) and \(X\sim P(m)\) with parameter m. The p.m.f. of X is : \(P(X=x)=\frac{e^{-m}\cdot m^x}{x!},\ x=0,1,2,\ldots\)

\(P(X\ge 3)=1-P(X\lt 3)=1-\left[\square+\square+\square\right]=1-\left[\frac{e^{-0.2}(0.2)^0}{0!}+\frac{e^{-0.2}(0.2)^1}{1!}+\frac{e^{-0.2}(0.2)^2}{2!}\right]\)

\(=1-[0.8187(1+0.2+0.02)]=1-\square=\square\)