Math Problem Statement
Solution
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Math Problem Analysis
Mathematical Concepts
Probability Density Function
Binomial Distribution
Chebyshev's Inequality
Expected Value
Variance
Formulas
f(x) = kx^2(4 - x^2)
P(X = k) = (n choose k) * p^k * (1 - p)^(n-k)
Chebyshev's Inequality: P(|X - μ| > kσ) ≤ 1/k^2
Theorems
Chebyshev's Inequality
Binomial Distribution Theorem
Suitable Grade Level
University Level
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