Math Problem Statement

Define a continuous random variable by the following probability distribution function:

f(x)=f(x)= 7929 x27929 x2 for 1≤x≤1≤x≤ 79507950 ,

and f(x)=0f(x)=0 for all other xx.

(i) Find E[X]E[X], giving the answer accurate to at least 2 decimal places.     (ii) Find E[X2]E[X2], giving the answer accurate to at least 2 decimal places.

  (iii) Hence find Var(X)Var(X), giving the answer accurate to at least 2 decimal places.    

Solution

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Math Problem Analysis

Mathematical Concepts

Probability
Continuous Random Variables
Expected Value
Variance

Formulas

Probability Density Function (PDF)
Expected Value (E[X])
Variance (Var(X))

Theorems

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Suitable Grade Level

Advanced undergraduate level

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