If the range of a random variable X is 0,1,2,3,4, with P(X=k)= (k+1) a 3^k for k 0 , then a is equal to

Step-by-step solution

Given that P(X=k)= (k+1) a 3^k for x (0,1,2, ) As we know that P(0)+P(1)+P(2)+ =1 aligned S & =a (1+ 2 3 + 3 3^2 + 4 3^3 + ) 1 3 S & =a ( 1 3 + 2 3^2 + 3 3^3 + ) S- 1 3 S & =a (1+ 1 3 + 1 3^2 + 1 3^3 + ) 2 3 S & =a ( 1 1- 1 3 ) 2 3 S & = 3 a 2 S & = 9 a 4 aligned From equation (i) array llrl & & 9 a 4 & =1 & a & = 4 9 array