Math Problem Statement
Let X be a discrete random variable. Then �(0 < � ≤ 2) must equal �(� = 1) + �(� = 2). 6) _F
Solution
This statement is True. Here's why:
For a discrete random variable X, the probability can be rewritten as:
This is because is discrete, so it takes on only specific values (such as integers). The interval includes the values and , but not .
Final Answer: True
Would you like further clarification on this? Here are some related questions for deeper exploration:
- What is the difference between discrete and continuous random variables?
- How does the concept of cumulative distribution functions (CDFs) relate to this problem?
- Can you express in terms of the probability mass function (PMF)?
- How would this differ if were a continuous random variable?
- Can you compute , and how would it differ from ?
Tip: Always identify the type of random variable (discrete or continuous) before applying probability rules.
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Math Problem Analysis
Mathematical Concepts
Probability Theory
Discrete Random Variables
Formulas
P(a < X ≤ b) = P(X = a+1) + P(X = a+2) + ... + P(X = b)
Theorems
Probability Mass Function (PMF)
Properties of Discrete Random Variables
Suitable Grade Level
Grades 11-12
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