Let X be a discrete random variable. Then �(0 < � ≤ 2) must equal
�(� = 1) + �(� = 2).
6) ___F__

This statement is **True**. Here's why:

For a discrete random variable **X**, the probability \( P(0 < X \leq 2) \) can be rewritten as:

\[
P(0 < X \leq 2) = P(X = 1) + P(X = 2)
\]

This is because \( X \) is discrete, so it takes on only specific values (such as integers). The interval \( 0 < X \leq 2 \) includes the values \( X = 1 \) and \( X = 2 \), but **not** \( X = 0 \).

### Final Answer: **True**

Would you like further clarification on this? Here are some related questions for deeper exploration:

1. What is the difference between discrete and continuous random variables?
2. How does the concept of cumulative distribution functions (CDFs) relate to this problem?
3. Can you express \( P(a < X \leq b) \) in terms of the probability mass function (PMF)?
4. How would this differ if \( X \) were a continuous random variable?
5. Can you compute \( P(0 \leq X \leq 2) \), and how would it differ from \( P(0 < X \leq 2) \)?

**Tip**: Always identify the type of random variable (discrete or continuous) before applying probability rules.

Let X be a discrete random variable. Then P(0 < X ≤ 2) must equal P(X = 1) + P(X = 2).

Explore the probability P(0 < X ≤ 2) for a discrete random variable X, with a detailed explanation of why it equals P(X = 1) + P(X = 2). Learn key concepts in probability theory, including the PMF and properties of discrete random variables. Suitable for Grades 11-12.

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