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Fit a Binomial distribution to the following data

Fit a Binomial distribution to the following data

x 0 1 2 3 4 5 6
F 5 18 28 12 7 6 4
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$\bar{X}$ = $\frac{∑(f_i x_i)}{N}$ = $\frac{(0+18+56+36+28+30+24)}{80}$ = $\frac{192}{80}$ = 2.4

$ p = \frac{\bar{X}}{n} = \frac{2.4}{6} = 0.4 $

∴ q = 1-p = 1-0.4 = 0.6

The Binomial distribution is p(X=x) = $^nC_x p^x q^{n-x}$ = $^6C_x (0.4)^x (0.6)^{6-x}$

i.e. Expected frequency = $N P(X=x)$ = $80 . 6C_x(0.4)^x (0.6)^{6-x}$

$$ \begin{array}{|c|c|c|c|c|c|c|} \hline x & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline f & 4 & 15 & 25 & 22 & 11 & 3 & 0 \\ \hline \end{array} $$

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