Answer:
Yes, because the sum of all of the probabilities is 1.
Step-by-step explanation:
The given probability equation is:
[tex]P(x)=\frac{2x-1}{16}[/tex], where x belongs to {1,2,3,4}.
[tex]P(1)=\frac{2(1)-1}{16}=\frac{1}{16}[/tex]
[tex]P(2)=\frac{2(2)-1}{16}=\frac{3}{16}[/tex]
[tex]P(3)=\frac{2(3)-1}{16}=\frac{5}{16}[/tex]
[tex]P(4)=\frac{2(4)-1}{16}=\frac{7}{16}[/tex]
Let us sum all the probabilities to obtain;
[tex]P(1)+P(2)+P(3)+P(4)=\frac{1}{16}+ \frac{3}{16}+\frac{5}{16}+\frac{7}{16}[/tex]
[tex]P(1)+P(2)+P(3)+P(4)=\frac{1+3+5+7}{16}[/tex]
[tex]P(1)+P(2)+P(3)+P(4)=\frac{16}{16}[/tex]
[tex]P(1)+P(2)+P(3)+P(4)=1[/tex]
Since the sum of all the probabilities is 1, it is a probability distribution
