Question

The binomial distribution for which mean = 6 and variance = 2, is

• A. $\left( \frac { 2 } { 3 } + \frac { 1 } { 3 } \right) ^ { 6 }$
• B. $\left( \frac { 2 } { 3 } + \frac { 1 } { 3 } \right) ^ { 9 }$
• C. $\left( \frac { 1 } { 3 } + \frac { 2 } { 3 } \right) ^ { 6 }$
• D. $\left( \frac { 1 } { 3 } + \frac { 2 } { 3 } \right) ^ { 9 }$

Answer 1

Answer: (D)

$\left( \frac { 1 } { 3 } + \frac { 2 } { 3 } \right) ^ { 9 }$

Answer 2

$n p = 6$

$n p q = 2 \Rightarrow q = \frac { 1 } { 3 } , p = \frac { 2 } { 3 }$ and $n = 9$

Hence the binomial distribution is $\left( \frac { 1 } { 3 } + \frac { 2 } { 3 } \right) ^ { 9 }$