Math Problem Statement
rewrite this pmf of X
Rewrite this PMF of X.
Solution
The PMF (Probability Mass Function) of provided in the table can be rewritten mathematically as:
\begin{cases} 0.1, & \text{if } x = 1, \\ 0.3, & \text{if } x = 2, \\ 0.2, & \text{if } x = 3, \\ 0.4, & \text{if } x = 4, \\ 0, & \text{otherwise.} \end{cases}$$ This expresses the probabilities for each value of $$X$$, with $$P(X = x) = 0$$ for any $$x$$ not explicitly listed. Let me know if you'd like further clarification! --- ### Relative Questions: 1. How is the PMF $$P(X = x)$$ related to the cumulative distribution function (CDF)? 2. What are the properties that a valid PMF must satisfy? 3. Can this PMF represent a continuous random variable? Why or why not? 4. How can we verify that this is a valid PMF mathematically? 5. What is the expected value $$\mathbb{E}[X]$$ for this PMF? ### Tip: Always check that the probabilities in a PMF sum up to 1 to ensure its validity!Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Probability
Probability Mass Function (PMF)
Formulas
P(X = x) = { 0.1 if x = 1, 0.3 if x = 2, 0.2 if x = 3, 0.4 if x = 4, 0 otherwise }
Theorems
PMF Definition
Total Probability Rule
Suitable Grade Level
Grades 9-12
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