Math Problem Statement

Find the mean value of the random variable whose pdf is given by F(x) =3 by 5 10^5 x (100-x), 0≤x≤100 The correct answer is 50

Solution

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Math Problem Analysis

Mathematical Concepts

Probability Density Function (PDF)
Expected Value
Integration

Formulas

Mean of a random variable: E[X] = ∫ x * f(x) dx
Given PDF: f(x) = (3/5) * 10^5 * x(100 - x), for 0 ≤ x ≤ 100

Theorems

Properties of PDFs
Fundamental Theorem of Calculus

Suitable Grade Level

University level (Probability and Statistics)