Mumbai University > COMPS > Sem 4 > Applied Mathematics 4

Marks : 06

Year : MAY 2015

Binomial distribution is applied only in those experiments which have exactly 2 outcomes. A dice has 6 equally likely outcomes.

Assume ‘x’ to be a binomial variate, then its first value should be zero and not one. This problem is solved just for the sake of solving

Mean $=\dfrac {\sum f_ix_i}{\sum f_i}=\dfrac {503}{132}=3.8106$

But, for binomial distribution, mean = np

$$3.8106 = 6p$$

$P = 0.6351 \\ Q = 1 – p = 1 – 0.6351 = 0.3649 \\ N = 6 \space \space and \space \space N = 132 \\ P (X = x) = \space ^n(x p^xq^{n – x} = \space ^6(_x x (0.6351)^x x (0.3649)^{6 – x} \\ \text { Theoretical frequency } = N \space x\space p (X = x)\\ = 132 x \space ^6(_x x (0.6351)^x x (0.3649)^{6 – x}$