Discussion
The mean and variance of a binomial distribution are 8 and 4 respectively, then the parameters are .............., ................... .
Answer: C
The parameters are n = 16, p = 0.5.
For a binomial distribution the mean is np and the variance is npq, with q = 1 - p:
\[ \begin{aligned} np &= 8,\quad npq = 4 \\ q &= 4/8 = 0.5 \\ p &= 0.5,\quad n = 8/0.5 = 16 \end{aligned} \]
Check: 16 \(\times\) 0.5 = 8 and 16 \(\times\) 0.5 \(\times\) 0.5 = 4. The pair n = 8, p = 0.5 gives a mean of only 4, and the pairs with p = 0.4 give a mean of 1.6 or 6.4, so none of them matches.
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