A random variable X takes values 0,1,2,3, with probability P(X=x)=K(x+1) ( 1 5 )^x , where K is constant, then P(X=0) is

Step-by-step solution

Given, P(X=x)=K(x+1) ( 1 5 )^x To find, P(X=0) Since sum of all the probabilities in a probability distribution is 1 . P(X=0)+P(X=1)+P(X=2)+ =1 K(0+1)(1 / b)^0+K(1+1) ( 1 5 )^1+K(2+1) ( 1 5 )^2+ =1 array ll & K+2 K ( 1 5 )+3 K ( 1 5 )^2+ =1 & K [1+2 ( 1 5 )+3 ( 1 5 )^2+ ]=1 array Let r=1 / 5K [1+2 r+3 r^2+ ]=1 aligned & K(1-r)⁻² & =1 & K (1- 1 5 )⁻² & =1 aligned K= 16 25 P(X=0)= 16 25 (0+1) ( 1 5 )^0= 16 25