Question

The variance of the Binomial distribution with probability mass function $p(x) = {}^{15}C_x \left(\frac{2}{3}\right)^x \left(\frac{1}{3}\right)^{15-x}$, $x = 0,1,\dots,15$, is _______}

• A. $\frac{5}{3}$
• B. $\frac{10}{3}$
• C. $\frac{1}{3}$
• D. $\frac{2}{3}$

Hint:

For any Binomial distribution:
Mean = $np$, Variance = $npq$.
Since $q = 1-p < 1$, the variance of a binomial distribution is always less than its mean.
Here, Mean = 10, Variance = 10/3.

Answer 1

The Correct Option is B