If the probability that the random variable X takes the value x is given by P(X=x)=k(x+1) 3^ -x , x =0,1,2,3 , where k is a constant, then P ( X 3) is equal to

Step-by-step solution

_ x=0 ^ k(x+1) 3^ -x =1 1 k =1+ 2 3 + 3 3^2 + 4 3^3 + ...(i) 1 3 k = 1 3 + 2 3^2 + 3 3^3 + ...(ii) (i)- (ii) 1 k - 1 3 k =1+ 1 3 + 1 3^2 + aligned & k = 4 9 & P ( x 3)=1- P ( x =0)- P ( x =1)- P ( x =2) & =1- k (1+ 2 3 + 3 9 )= 1 9 aligned