A set of numerical values assigned to a sample space is called
a. Random experiment
b. Random sample
c. Random variable
d. None of the above
The correct answer and explanation is :
The correct answer is: c. Random variable
Explanation:
In probability and statistics, a random variable is a fundamental concept. It refers to a set of numerical values that are assigned to the outcomes of a random process or experiment. Essentially, a random variable maps every outcome in the sample space to a real number.
Let’s break this down:
- A sample space is the set of all possible outcomes of a random experiment. For example, when tossing a coin, the sample space is {Heads, Tails}.
- A random variable takes these outcomes and assigns them numerical values. For example, you could define a random variable ( X ) where ( X = 1 ) if the coin lands on Heads and ( X = 0 ) if it lands on Tails.
There are two main types of random variables:
- Discrete random variables, which take on countable values (like 0, 1, 2, 3, etc.).
- Continuous random variables, which can take on any value within a given range (like any real number between 0 and 1).
Now, let’s quickly review the other options:
- a. Random experiment: This refers to any action or process that leads to a set of outcomes. Tossing a die is a random experiment, but it does not involve assigning numerical values by itself.
- b. Random sample: This refers to a set of observations drawn from a population, often used for making statistical inferences. It is different from assigning numbers to outcomes.
- d. None of the above: Incorrect, because random variable is the correct answer.
Thus, a set of numerical values assigned to a sample space is properly called a random variable, and it plays a critical role in linking real-world experiments to mathematical models in probability and statistics.