We call a discrete probability distribution if the distribution verifies.
• 0 ≤ P(X = x) ≤ 1
,
• ∑P(X = x) =1
This means that each probability must be lower or equal to 1 and more and equal to 0, and, the sum of all probabilities must be equal to 1.
We can see that all 3 values of P(X = x) in the table are less than 1.
Let's see if they add up to 1:
[tex]\Sigma P(X=x)=\frac{5}{8}+\frac{3}{4}+\frac{1}{4}=\frac{5}{8}+1=\frac{5}{8}+\frac{8}{8}=\frac{13}{8}[/tex]
Thus, the distribution is NOT a discrete probability distribution.
And the reason is
Since the sum of the probabilities is NOT equal to 1.
