Probability distribution of random variable X is X 0 1 2 3 4 5 P(X) 3…

The correct answer is Option (3) - $k=\frac{1}{9}$

$∑P(x_i)=1$

$3k+3k+2k+2k^2+3k^2+4k^2=1$

$8k+9k^2-1=0$

$9k^2+9k-k-1=0$

$9k(k+1)-1(k+1)=0$

$k=\frac{1}{9}$