If a discrete random variable X is defined as follows P [ X =x]= array cl k (x+1) 5^x , & if x=0,1,2 0, & otherwise array . then k =

Step-by-step solution

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