Answer to Question #283552 in Statistics and Probability for Ishu

Question

The following data shows frequency distribution of error page of a book. Fit Poisson distribution to the following :

Number error - 1,2,3,4,5,6,7,8

Frequency-12,18,19,05,09,14,12,11

Answer 1

$$\def\arraystretch{1.5} \begin{array}{c:c:c:c:c} x_i & f_i & x_if_i & P(X=x_i) & Expected\\ & & & & value\\ \hline 1 & 12 & 12 & 0.060161 & 6 \\ \hdashline 2 & 18 & 36 & 0.128143 & 13 \\ \hdashline 3 & 19 & 57 & 0.181963 & 18 \\ \hdashline 4 & 5 & 20 & 0.193791 & 19 \\ \hdashline 5 & 9 & 45 & 0.165110 & 17\\ \hdashline 6 & 14 & 84 & 0.117228 & 12 \\ \hdashline 7 & 12 & 84 & 0.071341 & 7 \\ \hdashline 8 & 11 & 88 & 0.037989 & 4 \\ \hdashline 9 & & & 0.044274 & 4 \\ \hdashline \end{array}$$

$$mean=\mu=\dfrac{\sum_ix_i f_i}{\sum_if_i}=\dfrac{426}{100}=4.26$$

$$\lambda=\mu=4.26$$

$$P(X=x_i)=\dfrac{e^{-\lambda}\cdot\lambda^{x_i}}{(x_i)!}$$