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

Step-by-step solution

aligned & We have, _ x=0 ^ P ( X =x)=1 & k _ x=0 ^ (x+1) ( 1 5 )^x=1 & k [1+2 ( 1 5 )+3 ( 1 5 )^2+4 ( 1 5 )^3+ ]=1 & k [ 1 1- 1 5 + 1 1 5 (1- 1 5 )^2 ]=1 aligned [ array r a+(a+d) r+(a+2 d) r^2+ . = a 1-r + d r (1-r)^2 array ] aligned & k ( 5 4 + 5 16 )=1 & 25 k 16 = i & k = 16 25 aligned