Find the binomial distribution for which the mean is 4 and varian… - Vidyadip

Question

Find the binomial distribution for which the mean is 4 and variance 3.

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Answer

$\text{np} = \text{4 and npq} = 3 $$\therefore \text{q} = \frac{3}{4} \Rightarrow \text{p} = \frac{1}{4} $
$\text{np} = 4 \Rightarrow \text{n} \times\frac{1}{4}= 4 \Rightarrow \text{n} = 16$
$\text{For writing n} = 16, \text{p} = \frac{1}{4}, \text{q} = \frac{3}{4} \text{or P (r)} = 16_\stackrel{{C}}{{r}}\bigg(\frac{1}{4}\bigg)^{16 - r} , r = 0, 1, 2, \dots\dots16$

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