Question

Determine whether or not the distribution is a discrete probability distribution and select the reason why or why not

Answer 1

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:

`\Sigma P(X=x)=(5)/(8)+(3)/(4)+(1)/(4)=(5)/(8)+1=(5)/(8)+(8)/(8)=(13)/(8)`

Thus, the distribution is NOT a discrete probability distribution.

And the reason is

Since the sum of the probabilities is NOT equal to 1.