To complete a discrete probability distribution, the sum of all probabilities must equal 1. A discrete probability distribution is a mathematical function that maps outcomes to their associated probabilities, and it must adhere to specific rules:
- Each probability must be between 0 and 1 (inclusive).
- The sum of all probabilities in the distribution must equal 1.
Here’s a step-by-step guide to determine the required value of the missing probability:
- Identify Known Probabilities: First, list out all the known probabilities in your distribution. For instance, if you have probabilities P1, P2, and a missing probability Px, write down their values.
- Set Up the Equation: Write the equation that represents the requirement for a valid probability distribution:
P1 + P2 + Px + ... = 1. - Calculate the Sum of Known Probabilities: Add up all known probabilities. For example, if P1 = 0.2 and P2 = 0.5, then
Sum = P1 + P2 = 0.2 + 0.5 = 0.7. - Find the Missing Probability: Rearrange the equation to solve for the missing probability. Using the previous example, your equation will now look like this:
0.7 + Px = 1. To find Px, subtract the sum from 1:Px = 1 - 0.7 = 0.3. - Verify the Results: Ensure that the computed missing probability, along with the others, satisfies the conditions of a probability distribution. Check whether all probabilities are between 0 and 1, and that their total equals 1.
Once you’ve followed these steps and calculated the missing probability, your distribution should now be valid. For example, if your final probabilities are 0.2, 0.5, and 0.3, they add up correctly to 1, thus confirming that the distribution is complete!