Ans:
E(5X+2)=3
5*E(X)+2=3
E(X)=1/5=0.2
For a valid probability distribution,sum of probabilities should be 1:
2k+k+3k+0.3+0.1=1
6k+0.4=1
6k=0.6
k=0.1
Now,
E(X)=0.2
-2*0.2-1*0.1+0*3k+1*0.3+c*0.1=0.2
-0.4-0.1+0.3+c*0.1=0.2
-0.2+c*0.1=0.2
c*0.1=0.4
c=4
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