Understanding Discrete Random Variables

A discrete random variable is a variable whose value is obtained by counting. It can only take on a finite number of values or a countably infinite number of values. Think of it as variables where the outcomes are distinct and separate, often whole numbers.

Analyzing the Options

Option 1: Outcomes of coin tosses

When you toss a coin, the outcomes can be counted, such as the number of heads in a specific number of tosses (e.g., 0 heads, 1 head, 2 heads). These are distinct, countable values, making this a discrete random variable.

Option 2: Outcomes of tossing a die

Tossing a standard six-sided die results in specific, separate outcomes: 1, 2, 3, 4, 5, or 6. Since these are distinct and countable values, this represents a discrete random variable.

Option 3: Outcomes of finding electron in atom

This option relates to the position or state of an electron within an atom. The position of an electron is not limited to specific, separate values; it can theoretically exist at any point within a certain region (described by probability distributions). Measuring or describing the position involves continuous values, not counts. Therefore, this is typically considered related to a continuous random variable, not a discrete one.

Option 4: Outcomes of measuring radioactive alpha decay

This usually refers to counting the number of decay events within a specific time period. For example, you could count 0 decays, 1 decay, 2 decays, and so on. Since the outcome is a count, this is a discrete random variable.

Conclusion on Discrete Variables

Based on the analysis, the outcomes related to finding an electron in an atom (its position or state) are not typically represented by a discrete random variable because they are not restricted to distinct, countable values. The other options all involve countable outcomes.