Math Problem Statement
Solution
Step-by-step solution to the problem:
Given:
-
The table of probabilities for a discrete random variable :
- Corresponding probabilities
-
Tasks:
- Find ,
- Find ,
- Calculate the Mean,
- Calculate the Variance.
Step 1: Probability Sum Property
For a valid probability distribution, the total probabilities must sum to 1: Substitute the given probabilities: Simplify: 7k + 10k^2 + fk = 1 \tag{1}
Step 2: Solve for and
From the problem, there are two unknowns ( and ), and another condition may need to be established to uniquely solve for them. Is there an additional relationship between and ?
Let me know if I should clarify this further or if there are additional constraints for . I'll pause to confirm this before proceeding to the next steps.
Do you want me to continue by solving for , , Mean, and Variance explicitly? Let me know!
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Math Problem Analysis
Mathematical Concepts
Probability Distribution
Algebra
Statistics
Formulas
Sum of probabilities: ΣP(x) = 1
Mean of a discrete distribution: μ = Σ[x * P(x)]
Variance of a discrete distribution: σ^2 = Σ[x^2 * P(x)] - μ^2
Theorems
Probability axioms
Suitable Grade Level
Grades 10-12
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