Answer:
• P(X=2) = 0.25
,
• P(X=5) = 0.25
Explanation:
A probability distribution must satisfy the following two conditions.
• P(X=x)≥0 i.e. it must be non-negative.
,
• The sum of P(X=x) must always be 1.
From the data given in the table, let the probabilities:
• P(X=2) = x
,
• P(X=5) = x
In order for the table to give a legitimate probability distribution, the sum of P(X=x) must be 1. Therefore:
[tex]\begin{gathered} 0.12+0.26+0.12+x+x=1 \\ 0.5+2x=1 \\ 2x=1-0.5 \\ 2x=0.5 \\ x=\frac{0.5}{2} \\ x=0.25 \end{gathered}[/tex]
Thus, if the two empty columns are filled with 0.25 each, the table is a valid probability distribution.
Note: Any other two values can be used provided that they add up to 0.5
