Math Problem Statement
A random variable X has the following probability density function f(x) = 6x (1 - x) for 0 ≤ x ≤ 1. Visually, the distribution of X is demonstrated below.
Compute P(0.26 < X < 0.49) 0.3442 (Enter your answer to four decimals) (b) Compute P(0.82 ≤ X ≤ 1) 0.0613
Solution
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Math Problem Analysis
Mathematical Concepts
Probability
Calculus
Integration
Probability Density Function (PDF)
Formulas
P(a < X < b) = ∫[a to b] f(x) dx
f(x) = 6x(1 - x) for 0 ≤ x ≤ 1
Theorems
Fundamental Theorem of Calculus
Properties of Probability Density Functions
Suitable Grade Level
Undergraduate (Introductory Probability/Statistics)
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