# Independent, Dependent and Controlled Variables ### Independent and Dependent Random Variables **Independent Random Variables:** * **Definition:** Random variables $$X$$ and $$Y$$ are independent if the occurrence of one does not affect the probability distribution of the other. * **Example:** Let $$X$$ be the outcome of rolling a fair six-sided die, and $$Y$$ be the outcome of flipping a fair coin. These events are independent since the outcome of the die roll does not influence the coin flip. **Dependent Random Variables:** * **Definition:** Random variables $$X$$ and $$Y$$ are dependent if the occurrence of one affects the probability distribution of the other. * **Example:** Let $$X$$ be the amount of rainfall on a given day, and $$Y$$ be the water level in a nearby river. These variables are dependent because more rainfall likely increases the river's water level. In a science experiment, there are three main types of variables, besides independent and dependent variables there is also the controlled variables. The **independent variable** is the one that the researcher deliberately changes or manipulates. Its purpose is to observe the effect it has on another variable. For example, in an experiment testing the effect of light on plant growth, the amount of light is the independent variable. The **dependent variable** is the one that is measured or observed in response to changes in the independent variable. Its purpose is to assess the effect of the independent variable. In the same plant growth experiment, the height of the plants is the dependent variable. **Controlled variables** are variables that are kept constant throughout the experiment to ensure that the test results are reliable. The purpose of controlling these variables is to make sure that any observed changes in the dependent variable are due to the manipulation of the independent variable alone. In the plant growth experiment, controlled variables might include the type of plant, the amount of water given, the soil type, and the ambient temperature. {% embed url="" %} --- # Agent Instructions: Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. Perform an HTTP GET request on the current page URL with the `ask` query parameter: ``` GET https://edu.abi.am/statistics-theory/random-variables/independent-dependent-and-controlled-variables.md?ask= ``` The question should be specific, self-contained, and written in natural language. The response will contain a direct answer to the question and relevant excerpts and sources from the documentation. Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.