Answer:
The set of probabilities associated with the values in a random variable's sample space is called the probability distribution. It provides the probability of each possible outcome or value that the random variable can take.
Explanation:
The probability distribution can be represented in various forms, depending on the type of random variable. For discrete random variables, the probability distribution is often presented as a probability mass function (PMF), which assigns a probability to each possible value. For continuous random variables, the probability distribution is typically described by a probability density function (PDF), which specifies the likelihood of the variable falling within a certain range of values.
For example, let's consider a random variable X that represents the outcome of rolling a fair six-sided die. The sample space of X consists of the values {1, 2, 3, 4, 5, 6}. The probability distribution or PMF for X would assign a probability to each of these values.
Assuming the die is fair, each outcome has an equal probability of occurring, so the PMF for X would be:
P(X = 1) = 1/6
P(X = 2) = 1/6
P(X = 3) = 1/6
P(X = 4) = 1/6
P(X = 5) = 1/6
P(X = 6) = 1/6
These probabilities sum up to 1, indicating that the probabilities assigned to all possible values of X cover the entire sample space.