A random variable X takes the values 0,1,2,3 and its mean is 1.3. If P ( X =3)=2 P ( X =1) and P(X=2)=0.3 , then P(X=0) is

Step-by-step solution

Given, P ( X =3)=2 P ( X =1) and P ( X =2)=0.3...(i) Now, mean =1.3 aligned & 0 P ( X =0)+1 P ( X =1)+2 P ( X =2) & +3 P ( X =3)=1.3 & 7 P ( X =1)=0.7 & ...[From (i)] & P ( X =1)=0.1 & Also, P ( X =0)+ P ( X =1)+ P ( X =2) & + P ( X =3)=1 & P ( X =0)+3 P ( X =1)=0.7 [ From (i) ] & P ( X =0)+0.3=0.7 & P ( X =0)=0.4 aligned