Subject: Applied Mathematics 2

Topic: Probability Distribution

Difficulty: High

Fit a poisson distribution to the following data

Fitting Poisson distribution means finding expected frequencies of x = 0 ,1 ,2 ,3, 4, 5, 6, 7, 8

Now mean = m = $\frac{∑f_i x_i}{N}$ = $\frac{(0+156+264+276+148+110+24+0+8)}{500}$ = $\frac{986}{500}$ = 1.97

∴ Poisson distribution of X is

P(X=x) = $\frac{(e^{-m}×m^x)}{x!}$ = $\frac{(e^{-1.97} × 1.97^x)}{x!}$

Expected frequency = N. P(x) = 500.$\frac{(e^{-1.97} × 1.97^x)}{x!} $

Putting x = 0, 1, 2, 3, 4, 5, 6, 7, 8, we get,

$$\begin{array}{|c|c|c|c|c|c|c|c|c|c|} \hline x & 0 &1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline f & 70 & 137 & 135 & 89 & 44 & 17 & 6 & 2 & 0 \\ \hline \end{array}$$