Question

In a binomial distribution, if ‘n' is the number of trials and ‘p' is the probability of success, then the variance is given by

Answer 1

SOLUTION

GIVEN

In a binomial distribution, if ‘n' is the number of trials and ‘p' is the probability of success,

TO DETERMINE

The variance

EVALUATION

If a trial is repeated n times and p is the probability of a success and q that of failure then the probability of r successes is

$\displaystyle \sf{ \sf{P(X=r) = \: \: }\large{ {}^{n} C_r}\: {p}^{r} \: \: {q}^{n - r} } \: \: \: \: \: where \: q \: = 1 - p$

So variance

= npq

= np(1-p)

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