A random variable X has the following probability distribution :
| x | 1 | 2 | 3 | 4 | 5 |
| P(X=x) | $K$ | $K$ | $3K$ | $2K^2$ | $4K^2$ |
Based on the above information, the value of 'K' is :
Answer & explanation
Correct answer: option 1
$\text{Total probability}=1.$
$K+K+3K+2K^2+4K^2=1.$
$5K+6K^2=1.$
$6K^2+5K-1=0.$
$K=\frac{-5+\sqrt{25+24}}{12}=\frac{-5+7}{12}=\frac{1}{6}.$
$K=\frac{1}{6}.$