Which of the following tables represents the probability distribution of X?Table ATable BTable CTable D

To determine which table represents a valid probability distribution of a random variable $X$, it is important to keep in mind two key rules that the probabilities must satisfy:

1. The sum of all probabilities must equal 1.
2. Each probability must be between 0 and 1 (inclusive).

Step 1: Analyze Each Table

1. Table A: Check the sum of probabilities and if all values are between 0 and 1.
2. Table B: Similarly, assess the probabilities in this table.
3. Table C: Perform the same summation and check conditions.
4. Table D: Finally, evaluate the probabilities in this table.

Step 2: Sum Calculation

For each table, sum the probabilities to check:

$\text{Sum of probabilities} = P(X_1) + P(X_2) + P(X_3) + \ldots + P(X_n)$

Step 3: Determine Valid Table

Upon calculating and analyzing the sums for each table, the one that meets both criteria will be the correct probability distribution table for $X$.

Final Answer

Once the evaluations are complete, the table that satisfies the above conditions (summing to 1 and probabilities in the range of [0, 1]) is the answer. If you can provide the probability values for each table, I can conduct the analysis and definitively identify which one is correct.