csat-suneung 2019 Q8

csat-suneung · South-Korea · csat__math-science 3 marks Binomial Distribution Find Parameters from Moment Conditions
When the random variable $X$ follows the binomial distribution $\mathrm { B } \left( n , \frac { 1 } { 2 } \right)$ and satisfies $\mathrm { E } \left( X ^ { 2 } \right) = \mathrm { V } ( X ) + 25$, what is the value of $n$? [3 points]
(1) 10
(2) 12
(3) 14
(4) 16
(5) 18
When the random variable $X$ follows the binomial distribution $\mathrm { B } \left( n , \frac { 1 } { 2 } \right)$ and satisfies $\mathrm { E } \left( X ^ { 2 } \right) = \mathrm { V } ( X ) + 25$, what is the value of $n$? [3 points]\\
(1) 10\\
(2) 12\\
(3) 14\\
(4) 16\\
(5) 18