Check whether the following is a valid probability mass function or not.

$p(x)=\frac{x^2-x}{16},x=-2,-1,0,1,2,3.$

I have attached answer rto the question below.

$(1)0$

$(i)=\frac{1}{3}$

$(1)-\frac{3}{8}$

Since $T(x)0$ for all values of $x,$ the first cond rims is satisfiot.

$vA(x)=\frac{3}{8}+\frac{1}{8}+0+a+\frac{1}{x}+\frac{3}{8}=1$

Therefore, second condition is also satisfied.

Hense, the given fanction is a valid probohility mass furction.