Final answer:
To create a legitimate probability distribution for the discrete random variable X with possible values of -3, -1, 3, 5, and 6, you need to assign probabilities to these values that satisfy the conditions of non-negativity and summing to 1.
Step-by-step explanation:
To create a legitimate probability distribution for the discrete random variable X with possible values of -3, -1, 3, 5, and 6, you need to assign probabilities to these values that satisfy the following conditions:
- Each probability must be non-negative.
- The sum of all probabilities must equal 1.
An example of a legitimate probability distribution for X could be:
- P(X=-3) = 0.1
- P(X=-1) = 0.2
- P(X=3) = 0.4
- P(X=5) = 0.1
- P(X=6) = 0.2
These probabilities are all non-negative and their sum is equal to 1. This is a valid probability distribution for X.