Mumbai University > COMPS > Sem 4 > Applied Mathematics 4

Marks : 08

Year : DEC 2015

Fitting poisons distribution means finding expected frequencies of

$X: 0, 1, 2,3,4,5,6,7,8$

Now mean $=\dfrac {\sum bixi}{\sum Bi}=m\\ \sum Bixi=500=N\\ \therefore m=\dfrac {986}{500}=1.972$

Poissons distribution of x is

$P(X=x)=\dfrac {e^{-m}\times m^x}{x!}=\dfrac {e^{-1.972}\times (1.972)^x}{x!}$

Expected frequency $=N\times P(x)\\ =500\times \dfrac {e^{-1.972}\times (1.972)^x}{x!}$

Now putting $X=0$

we get $P(X=0)=\dfrac {e^{-1.972}\times 1}{0!}=0.1392$

Expected frequency $N\times P =500 \times 0.1392\\ =70$

Similarly

When $x=1, 2,3,4,5,6,7,8$

We get

$B(x)=137,135,89,44,17,6,2,0$ resp.

$\therefore $ Poisson distribution