Question
Determine whether the values given below are appropriate as the values of a probability distribution of a discrete random variable $X$, which assumes the values $1,2,3$ and $4$ only.
$(i)\ p(1)=0.25, p(2)=0.75, p(3)=0.25, p(4)=-0.25$
$(ii)\ p(1)=0.15, p(2)=0.27, p(3)=0.29, p(4)=0.29$
$(iii)\ p(1)=\frac{1}{19}, p(2)=\frac{9}{19}, p(3)=\frac{3}{19}, p(4)=\frac{4}{19}$
$(i)\ p(1)=0.25, p(2)=0.75, p(3)=0.25, p(4)=-0.25$
$(ii)\ p(1)=0.15, p(2)=0.27, p(3)=0.29, p(4)=0.29$
$(iii)\ p(1)=\frac{1}{19}, p(2)=\frac{9}{19}, p(3)=\frac{3}{19}, p(4)=\frac{4}{19}$