Math Problem Statement
Let X X be a continuous random variable with PDF: f X ( x )
{ 5 x 4 0 < x ≤ 1 0 otherwise f X (x)={ 5x 4
0
0<x≤1 otherwise
Find P ( X ≤ 3 9 ∣ X
1 9 ) . P(X≤ 9 3 ∣X> 9 1 ).Enter your answer correct to three decimals accuracy.
Solution
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Math Problem Analysis
Mathematical Concepts
Probability Theory
Conditional Probability
Probability Density Functions (PDF)
Cumulative Distribution Functions (CDF)
Formulas
P(A | B) = P(A ∩ B) / P(B)
CDF F_X(x) = ∫ f_X(t) dt
PDF: f_X(x) = 5x^4 for 0 < x ≤ 1
Theorems
Law of Total Probability
Conditional Probability Theorem
Suitable Grade Level
Undergraduate Probability/Statistics
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